I have no clue where the oldest copy of the Codex is. Additionally, are you asking about the Codex or the entirety of the Corpus Iuris Civilis? The Codex is only 1/3 of the Corpus, which also includes the Institutes and the Digest. The other thing to note is that an entire Corpus is going to be a very, very rare thing in the Middle Ages. It's real long in published form today, imagine how many animals would have to die for parchment pages and an extraordinary amount of manpower copying everything down. It is likely that most people would have used extracts.

The Digest was supposedly rediscovered in Rome sometime during the 11th century and the University of Bologna was established in part to study it. This is the beginning of the age of the glossators. With that in mind, you might find a copy on display in the Medieval Museum of Bologna, which has codices on display. I've been to many museums in Italy (not Bologna yet, but I'm going this spring) and I don't recall any copies of any part of the Corpus, but the collections of so many of these museums run together in my mind with only the most standout pieces able to be recalled easily.

Check out this book: https://www.worldcat.org/title/corpus-iuris-civilis-in-the-middle-ages-manuscripts-and-transmission-from-the-sixth-century-to-the-juristic-revival/oclc/848781265&referer=brief_resultsrevival/oclc/848781265&referer=brief_results.

This volume should tell you where the earliest bits and pieces of the codex can be found in the medieval west, but my guess would be that there are older versions somewhere in the eastern Mediterranean where it was originally compiled.