How do I replicate simulations on a research paper?
If you don't have the original code, you need to use the experiment descriptions (the methodology) to create your own code, and perhaps data. This is much harder, of course, than if you had the code. But it is much more valuable for science as a whole. If you come to the same results (statistically speaking) then you have evidence that the original hypotheses stand up. But if you get different results you have to question why. Either the original result was false or your own work misses something. Both cases lead to advances in science. 

And, running the same code on the same data is a bit boring, actually. Hardly something that can be published. 

But point your own efforts at the hypothesis in the original paper, not at the results specifically. Then, you have something publishable whether you confirm or refute the original results.