Question

What are limitations of Hammurabi's Code as evidence of life in Babylonia

Answer 1

The limitations of Habburabi's code as evidence if lift in Babylonia are that punishment was very much determined by the amount of evidence available, and how truthful the witnesses involved in the trial were. It also treated citizens very differently depending on their social status, and the punishments for crimes were determined by how high-ranking the victim was.
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Answer 2

The Code of Hammurabi can tell us much about ancient Babylonian society, but cannot show us everything.  The law code was written for the audience of Babylonian people in its own day, especially the scribes and officers of the law.  So there are many questions we would have from a distance much later in history that people then would have understood without needing explanation.  The intention of the law code was to inform people of laws and punishments, not to give later generations a full view of the whole of Babylonian life.  The law code was prepared by those in power in the government of Hammurabi -- we don't get any response from the people or indication of how the people then viewed the laws.  And ultimately, the law code is written in a detached, impersonal way -- as legal documents generally are written.  We don't get a feel for the personal lives or feelings of people living at that time in Babylonia.