How did Hammurabi justify this law code to the people he ruled?

Hammurabi justified his law code to the people by simply being himself. By claiming himself king and a servant of the god Marduk, he was imbued with the power to mete out justice in any way he saw fit throughout his lands. Initially, this was a simple matter, because Mesopotamia had not yet been unified; however, as Hammurabi absorbed more cities into his kingdom, he faced the unique challenge of winning over subjects who were not necessarily as committed to worshipping Marduk—or any god(dess)—as he was.
As a ruler, Hammurabi genuinely cared for the wellbeing of his current and future subjects, and so rather than rely upon the assumption that everyone served Marduk’s will, he codified his 282 eye-for-an-eye-style laws into a much more secular collection that still respected individual worshippers’ choices of patron deity. This way, there would be no confusion about one god or goddess requiring more or less in terms of punishments depending on the city of worship.
Hammurabi also recounted the divine inheritance of the laws in a prologue for the Code and peppered self-praise throughout the stele, lest his subjects forget how divine and merciful he was.
https://www.history.com/topics/ancient-history/hammurabi