Hammurabi's code brought a sense of fairness to his people and established order in society

The Hammurabi's Code integrates different subjects of the Law, i. e., not just one country but integrating traditions of various different people. The famous "eye for an eye" is actually a softening of previous behaviours, were private vengeance or blood feuds were common.

Yes, it is true that Hammurabi's Code brought a sense of fairness to his people and established order in society, since it established criminal codes and standards of punishment for thieves, among other things.