Re: No, no they don't.
" The "Code of Ur-Nammu" dates to ~2100-2050 BCE and specifies punishment for (among other crimes) murder, robbery, adultery and rape. Spoiler alert - the penalty for all of them is death."
I suspect given the conditions of that society (no such things as jails, for example, and no practical destination for an exile, etc.), death was basically the only option that would stick.
PS. In the end, laws are just ink on a page. What matters law to a charismatic sociopath able to raise a army big enough to overrun you?