Publishing a very mediocre paper as undergraduate?
So you want to publish rubbish, just to have a publication on your CV? If you really are a good student, you will find other ways to get publications. Remember that such a publication will stay with you forever, everyone googeling you will find it. On the other hand, once you have some publications, no one will care if you made your first one during your undergraduate or later.

Also: Talk to your professor. He will have reasons to decline and will be able to tell you more about the pros and cons of publishing this paper, given your academic plans. I would put quite some weight on his opinion, as he knows the paper and has lots of experience when it comes to the field, accepting or declining PhD students, etc.