How does the code of hammurabi illustrate key elements of what a civilization is?

Interesting question; the one problem in answering this is that people and researchers are still arguing over what are key elements of a civilization and what civilization itself. So, ultimately, this is a viewpoint question that depends on what you see as a civilization since it's such a debatable term and concept.

I, personally, don't think its very apparent, simply because I don't necessarily agree with the civilized/uncivilized dichotomy. Some key elements that this code reveals include the idea of writing, a written code of law, class and wealth distinctions, checks on judges, familial regulation, military affairs, and regulations on trade & commerce.

the government closely monitored its finances to avoid another financial collapse.

warfare was the primary means of cultural transmission in both regions.