What were the underlying principles of Hammurabi's code of laws?

Question

And what does the law code tell us about the kind of society that existed there at the time?

Answer 1

"eye for an eye"

Answer 2

Basically - "an eye for an eye and a tooth for a tooth." It's from Hammurabi's Code that this expression comes. There are several more - you'll have to look them up.

It's most important factor is that it was the first time Laws were Codified and applied to an entire civilization.