It was actually more of a tunic or robe; a similar thing called "toga" is still worn by lawyers and judges in the higher appeals courts in Italy.

Robes were fairly standard ceremonial patrician dress in Early Modern Italy, at least in the north; "Nobiltà di Toga," or "Nobility of the Toga/Roge" typically referred to a segment of the lower aristocracy or upper bourgeoisie who derived a lot of their wealth and influence from holding public office, and this certainly included the magistrature. An unverified etymology stems from the toga or robe worn by university graduates when undertaking their final examinations; a degree from a university, typically the University of Pavia in the aforementioned Milanese context, was often a prerequisite for many official appointments.

I can't find any helpful images of sixteenth century togas, but since you brought it up this is an example of toga worn by a high-level Venetian official (albeit in the eighteenth century, not sixteenth, plus they're particularly sumptuous; a Milanese magistrate would probably have worn simpler black robes).