If you have found an example in Luther's writings where he "argued salvation through good works", I would like to see it. Without a citation, it is difficult for me to respond to that particular point. In the meantime, I will try to give an account of Luther's views on justification. Most of my relevant books are in my office, so I'm not using ideal English versions (e.g. Luther's Works, American Edition) when citing here, FYI.

Here is some background information that I find necessary; feel free to skip it if you are short on time or feel confident of your knowledge of high medieval theology. Warning, this is a lot of background, so I have marked the paragraph where my answer begins with a !. To understand Luther's views on justification, you need to understand some of the theology he was reacting against. Let's discuss both context and terms. Luther appeared during a time of major debate in the western church over human agency in salvation, namely to what extent a human being could contribute to their own salvation. Salvation is being freed from the penalty of sin, namely damnation. In this context, contribution to one's salvation meant performing works of merit (i.e. "good works", more on this) which would in a sense counterbalance sins committed in life. Sins incurred guilt, merit reward, and thus good works along with the sacrament of confession played a part in counteract sin by contributing to the ultimate sanctification (i.e. becoming holy, like God) of a person. This work--of removing the penalty and guilt of sin in a person--is what is meant by justification, and being justified means being in a state in which the penalty and guilt of sin have been removed from you. We might also call the quality of this state righteousness. So, to summarize, there is an on-going debate over to what extent an individual has the agency and ability to contribute to their own justification, and thus salvation.

One side of this argument is what we would pejoratively refer to as semi-Pelagian (referencing a 5th century debate between Augustine of Hippo and Pelagius). Without going into the history behind the term, this view argued that by God's grace (that is, the free and undeserved gift), God chooses to accept certain good works as meritorious, meaning meriting forgiveness of the penalty of sin. They distinguished between two types of merit: condign and congruent. Condign merits were merits which were performed with the dignity of Christ; congruent merits were performed without. To perform a condign merit, most on this side believed one needed to be in a state of grace, that is, a state of having confessed and been forgiven of sin. An example of this would be a Christian, having confessed and been forgiven of their sins up to the present, performing a work of charity, such as giving alms to the poor, or attending mass. To perform a congruent merit, a state of grace was not required. An example of a congruent merit might be a person with unconfessed or a non-Christian aiding a neighbor. Congruent merits are often called quasi-merits, because they were not as efficacious an condign merits. Congruent merits were accepted by God freely out of mercy; condign merits were accepted by God out of obligation due to promises made to apply his Son's merits to his followers (this is why they are called condign, meaning with the dignity of Christ). The views on this side were that humanity had within itself the ability to merit salvation, for God had deigned to accept even the congruent merits of those in a state of sin; thus one needed only to do what is within themselves (facere quod in se est) and God would aid that effort to bring about salvation. Put another way, try your best, and God will do the rest.

On the other side of this debate were what we might call the strict Augustinians, i.e. those who held a greater adherence to the though of Augustine. Augustine argued that it was God who worked good in us, that by our own ability and will we were incapable of doing the good, and it was thus no good works could achieve salvation but only the grace of God. This group denied the existence of congruous merits and emphasized God's agency over human agency in condign merits. You can see how, in a way, both sides were operating within a framework, to wit God's grace is necessary to salvation. The question was how God's grace acted--was it the agent of salvation, or merely a facilitator.

! Luther was an Augustinian friar, so you can imagine which side he sided on. In many ways, he was as strict an Augustinian as you can find; indeed, one scholar has described the reformation as "the triumph of Augustine's doctrine of grace over Augustine's doctrine of church." (Calvin and Augustine by Benjamin Warfield, p.383) Luther argued for a hard-line approach to justification, namely that the human being is incapable of contributing to their own salvation, and that justification comes by God attributing it to the human being on account of faith as opposed to works of merit. Put simply, God declares you righteous. The term for such righteousness is alien righteousness (as opposed to proper righteousness) because it does not belong to a person as recompense for meritorious works but belongs solely to God and is merely attributed to the individual. The analogy Luther often uses of how this occurs is a marriage analogy where Christ is the groom and we the bride. By faith, we enter into a marriage to Christ in which he receives our sin (which were atoned for on the cross) and we receive his righteousness. Luther will often described the believer as covered by the righteousness of Christ such that when God looks at us he sees not our sin but the righteousness of Christ and imputes it to us. Details as to how Luther came to this position and how he reasoned it I will save for another day; if you would like to explore it for yourself, see his On the Freedom of a Christian or his On the Bondage of the Will or his Lectures on Galatians (1535).

Now, many accused Luther of being antinomian (i.e. against the law, which in this context would mean saying that good works don't matter and are irrelevant), but this was never the case. My guess is that something Luther wrote defending against that charge is what has thrown you off. In reality, Luther had a robust sense of the place for good works in the Christian life; the difference between Luther and those who came before him was that Luther viewed good works as the fruit of salvation rather than the means to salvation. For Luther, when you realized that God had done this amazing thing for you (i.e. become a human and died on the cross for you, setting you free from sin and death), you would naturally respond by going and doing likewise. God sets you free by grace to do good works. In a sense, Luther is concerned about genuine altruism, because under the high medieval system, everything good you do for someone else is really a good you do for yourself because it helps contribute to your salvation. In Luther's mind, God has no need of your good works. Rather, by faith God sets you free from concern over your salvation which liberates you to do good works. Luther appeals to the Gospel of Matthew (12:23) where Jesus talks about a good tree bearing good fruit and a bad tree bad fruit. Luther writes,

"Therefore, let the person who wishes to do good works begin not with the works but with the believing, for this alone makes a person good. For nothing is able to make a person good except faith, and nothing can make a person evil except unbelief. [...] Let it be understood that we do not reject good works. Indeed, good works are cherished and taught by us. We do not condemn them for their own sake but on account of this godless addition to them--namely, that righteousness is to be obtained through them." (cf. "On the Freedom of a Christian" in Martin Luther's Basic Theological Writings, ed. Lull and Russell, p.416, 417-418).

So, to address the possible source of your confusion, Luther does not reject or abandon good works, only what he views as their theologically incorrect role in the process of salvation. Receiving salvation as a free gift from God on account of faith for Luther sets one free to go and love with equal abandon: as God has been so gracious and loving with us, how can we but go and be likewise with other? Faith for Luther is the catalyst for the Christian life, not the culmination. In this, he is rejected the medieval distinction between unformed and formed faith, that is, faith formed by love and its corresponding works. For Luther, faith produces good works; it is not the product of them. This does not mean, however, that one with faith will never sin; we still endure the temptations of this world, for in faith we are both saint and sinner (simul iustus et peccator). Luther's theology redefines the relationship between faith and works; it does not reject the importance of works, only their relationship to salvation.

Sources / Further Reading:

The Theology of Martin Luther by Paul Althus (Fortress Press, 1966)

The Theology of Martin Luther: A Critical Assessment by Hans Martin Barth (Fortress Press, 2013)

The Harvest of Medieval Theology by Heiko Oberman (Harvard, 1963)

The Christian Tradition, Vol. IV by Jaroslav Pelikan (Chicago, 1984)