Before the Code of Hammurabi was written on a stone pillar for all to see, laws were held in peoples' memories and transmitted orally. Why would a written legal code be an improvement over an oral set of laws?

Oral sets of law were overwritten by the introduction of written legal codes. This is because written legal codes could be recorded and preserved for the future. They could not be distorted as they were written down and omitting the main subject was difficult. They had legal validity over oral laws, thus could not be easily denied.