Byzantine culture peaked in the sixth century under which Emperor?

Constantine

Charlemagne

Justinian I

Muhammad II

Byzantine culture peaked in the sixth century under "Justinian I" (also known as Justinian the Great), due mostly to the fact that this was when the empire was at its greatest physical size.

The correct answer to your question would be Justinian I. He was the Byzantine emperor that was revered by many at the time as he made significant advances in Byzantine society and law as well (we know that Justinian's code of law existed and was enforced for example). He was also called Justinian the Great, due to all the positive changes he brought upon to this empire.