Dude, this DOES NOT prove your point. Here's a quote from your link:
Hammurabi (1728 BC–1686 BC) believed he was chosen by the gods to deliver the law to his people. In the preface to the law code, he states, "Anu and Bel called by name me, Hammurabi, the exalted prince, who feared God, to bring about the rule of righteousness in the land."[1] In the upper part of the stela, Hammurabi is shown in front of the throne of the sun god Shamash.
How does that show religion had no place in their law?
A king at that period was mad if he didn't claim that some divine sourced "inspired" him, since kings claimed their throne through divine rule. If anything, kings took pre existing common law, and stamped their name on it along with a "divine source." Most laws at that time were collections of various regional common law.
"The Code of Hammurabi was one of many sets of laws in the
Ancient Near East. Most of these codes, coming from similar cultures and racial groups in a relatively small geographical area, necessarily have passages that resemble each other. The earlier code of Ur-Nammu, of the
Ur-III dynasty (21st century BC), the
Hittite code of laws (ca. 1300 BC), and
Mosaic Law (traditionally ca. 1200 BC under
Moses), all contain statutes that bear at least passing resemblance to those in the Code of Hammurabi and other codices from the same geographic area."
Also, its not a far off thought to see that all other regional laws and common law were inspired by this as well, and were gathered by rulers and put a big "THIS WAS GIVEN TO ME BY GOD!" stamp on it. All laws are secular, its just that some have been stolen by the religious and claimed to be given to them by a divine source.