Nearly 2 millennia, and it was itself preceded by quite a few centuries by the Code of Ur-Nammu.

That's not to say there's not a grain of truth in this perspective. My impression is that Romans were notable for their pioneering work in the field of what could best be described as "civic pride" - the sense that "civilization" represented progress, the idea of the state as a kind of collective project that elevates everyone and that we should all be proud to participate in. They probably weren't the first to think like this - history is long - but they were the last to do so in a largely secular fashion in the West for a long time, and certainly directly influenced the thoughts of the Enlightenment thinkers who eventually inspired the American Revolution.

S.P.Q.R.

The Code of Hammurabi isn't what it seems at first glance. Modern people naïvely read it like a legal code, but that interpretation doesn't hold up to scrutiny. It contains too many inconsistencies to be a practical legal code. One of the more obvious examples is the case of property given to another for safekeeping without a document documenting the arrangement. Is the recipient a thief who should be put to death? Or can the recipient keep the property without consequence because the alleged owner has no proof of anything? Furthermore, records concerning disputes contemporary with the Code of Hammurabi exist. Other than a single reference to a standard wage for weavers on the stele, records do not reference the code. Indeed, legal decisions are often inconsistent with the code.

The Code of Hammurabi is best understood as royal propaganda designed to portray Hammurabi as a just king. The famous stele starts with a graphic depiction of him receiving the royal rod and ring from Shamash, the sun god who was emblematic of truth and justice. The laws are best understood as a statement of the kind of justice Hammurabi wished to see done in his kingdom, not a set of rules.

Code of Hammurabi was created based on a whim of a single person (the namesake) and solely served to simplify administration. He could also always change it at will, or ignore for his own needs.

Rule-based society is something different: when the Law itself has a power of it's own, stronger than power of any individual or group. It was first invented in Rome and provided them tremendous advantage, until started to crumble during the Long 3rd Century Crisis.