Since you have not provided any further information so that I can answer your question, I will ask if this Google search has provided the information needed to base any response on with respect to Hammurabi: -
If this is the historical person you are wanting to compare with Abraham, then from my understanding, when using the information provided by Wikipedia, I can state that they were not living at the same time. Abraham lived 2150-1975 BC - and died around 150 years before Hammurabi was born.
On the other hand, the Oral Tradition of Israel suggest that Abraham and Nimrod were contemporaries in that Abraham's life overlapped Nimrod's life during the latter portion of Nimrod's life. This tradition suggests that Nimrod caused bot Terah and Abraham to Flee from Ur as Nimrod wanted to kill them both. They both probably also left Ur to ensure that Haran's estate passed to his son Lot and not to Haran's chief steward as was the custom at that time.
Wikipedia also suggests that Maruk was the name of a "god" of Babylon.
But I am sure that you already knew all of this.