There are substantial differences between the lessons of Jesus and the standards set forth by Hammurabi's code. Whereas the "Code" was intended to preserve order and establish justice, Jesus' teaching emphasized forgiveness and love of one another.
For example, Hammurabi's Code is based on the principle of lex talionis, (the law of retaliation.) The following language from the code is illustrative:
If a son strike his father, his hands shall be hewn off.
If a man put out the eye of another man, his eye shall be put out.
If he break another man's bone, his bone shall be broken.
This bears a strikng resemblance to the Old Testament doctrine of "an eye for an eye; a tooth for a tooth," etc.
Jesus, however stressed forgiveness, forbearance, and avoidance of confrontation:
You have heard that it was said, ‘An eye for an eye and a tooth for a tooth.’ But I say to you, Do not resist the one who is evil. But if anyone slaps you on the right cheek, turn to him the other also. And if anyone would sue you and take your tunic, let him have your cloak as well. And if anyone forces you to go one mile, go with him two miles. Give to the one who begs from you, and do not refuse the one who would borrow from you.
Hammurabi's Code also recognized social distinction; noblemen and freedmen were punished less severely than commoners and slaves. A commoner who injured a nobleman was put to death; yet a nobleman who injured a commoner was required to pay a fine in silver.
In contrast, Jesus drew no distinction between individuals:
You know that those who are regarded as rulers of the Gentiles lord it over them, and their high officials exercise authority over them. Not so with you. Instead, whoever wants to become great among you must be your servant, and whoever wants to be first must be slave of all.