What was the main idea behind the Hammurabi Code?

An eye for an eye.

There was a bit more to it than that.

Code of Hammurabi
Created c. 1792–1750 BC (middle chronology)
Location The Louvre, Paris, France (originally Sippar, Mesopotamia (modern-day Iraq), found at Susa, Iran)
Author(s) King Hammurabi of Babylon
Subject Law, justice
Purpose Debated: legislation, law report, or jurisprudence

The Code of Hammurabi is a Babylonian legal text composed during 1755–1750 BC. It is the longest, best-organised, and best-preserved legal text from the ancient Near East. It is written in the Old Babylonian dialect of Akkadian, purportedly by Hammurabi, sixth king of the First Dynasty of Babylon. The primary copy of the text is inscribed on a basalt stele 2.25 m (7 ft 4 1/2 in) tall. The stele was rediscovered in 1901 at the site of Susa in present-day Iran, where it had been taken as plunder six hundred years after its creation. The text itself was copied and studied by Mesopotamian scribes for over a millennium. The stele now resides in the Louvre Museum.

The top of the stele features an image in relief of Hammurabi with Shamash, the Babylonian sun god and god of justice. Below the relief are about 4,130 lines of cuneiform text: one fifth contains a prologue and epilogue in poetic style, while the remaining four fifths contain what are generally called the laws. In the prologue, Hammurabi claims to have been granted his rule by the gods "to prevent the strong from oppressing the weak". The laws are casuistic, expressed as "if ... then" conditional sentences. Their scope is broad, including, for example, criminal law, family law, property law, and commercial law.

Modern scholars responded to the Code with admiration at its perceived fairness and respect for the rule of law, and at the complexity of Old Babylonian society. There was also much discussion of its influence on the Mosaic Law. Scholars quickly identified lex talionis—the "eye for an eye" principle—underlying the two collections. Debate among Assyriologists has since centred around several aspects of the Code: its purpose, its underlying principles, its language, and its relation to earlier and later law collections. Despite the uncertainty surrounding these issues, Hammurabi is regarded outside Assyriology as an important figure in the history of law and the document as a true legal code.

https://en.wikipedia.org/wiki/Code_of_Hammurabi

The idea was that it was a legal code presented by Hammurabi to his kingdom, which emphasized the importance of doing justice and paying damage. Interestingly enough, Hammurabi's idea of justice - often compared with Exodus 21-23 and not unlike it - is still a bit more strict than the idea of "an eye for an eye". Hammurabi's code uses the death penalty as a deterant from all sorts of crimes, which makes the book of Exodus seem quite liberal in comparison.

Seems to me that the main idea behind the code was twofold: 1) by writing it in stone it became immutable, and 2) by posting it in the open it made the workings of the law open to all and no excuse would be allowed for ignorance.
The central theme of the codex was an entrenchment of the class structure, where stiffer penalties were incurred by lower class persons offending upper class persons and lighter penalties prevailed when the situation was reversed.