The final mitzvah commanded to all mankind was to establish courts of justice, not only to enforce the other six laws but also to legislate for the betterment of society.
This is another mitzvah we can see in action from before the Torah was given. When Shechem raped Dina in Genesis chapter 34, her brothers took it out on the entire city. Why? What did they do? Simple: they turned a blind eye to the crime. They refused to bring Shechem to trial, which made them guilty of failing to enforce justice.
This mitzvah includes many details that are separate commandments for Jews: to appoint judges, to treat the litigants equally, not to accept bribes, not to favor a VIP nor to rule based on compassion for a poor person, not to testify falsely, and more.