Should I continue with this research? I was appointed to make some programming outside of a research group to see if I can be accepted for doctoral studies. The task is to mimic the results of one paper and from that point to carry more research about it. 

Because of some personal problems, that project got delayed. The thing is that when I got the results of my program, and I compared with the ones that I was supposed to get, there were some differences (it was a medical related project). When I started comparing those differences I saw that some of my results were backed up by some medical papers.

Now the initial project has ended, because there has been published one software tool that do almost the same thing. And that research group is focusing on other projects.

My question is, is there any way I can publish the results I obtained with the program I made? I have spent more than six months doing that, without payment. How can I name it? Is it a model? Should it be published like a technical report? Any help will be great.
As JeffE said in his comment, you will need to seek permission from the director of the research group - if permission is given, I would suggest to get their input as to how to develop the research into a paper, and even suggest having the director as a co-author.