I submitted my own code on someone elses account I was flagged for plagiarism on a programming assignment. We get 3 submissions a day for the ~3 weeks that the project is open. I finished my project in about 1 week, but on one of those days I used my friend's computer to submit my assignment to the autograder (so I really got 4 submissions in one day). The undergraduate Honor Council at my college found me guilty of cheating on the assignment, and I'll have to report to another Honor Council with 5 professors evaluating my case and asking me questions to determine my ultimate punishment.

In all honestly, I just submitted on my friend's account to see if it would work (I was curious if they checked on submitting on peoples' accounts who weren't in the class). I still had ~2 weeks worth of submissions when I submitted my project for the final time, so I don't really think I had an unfair advantage over my peers.

Is this really a serious offense? The undergraduate council recommended to the official council that I get a 0 on the project (I actually got 100 on it), which would put me at a &lt;= C- in the class (which is failing) given how heavily weighted this assignment was, but this seems rather ridiculous given it was all my code.
Given that the student Honor Council has already found you guilty of cheating, maintaining that what you did was simply out of curiosity does not seem like a good strategy.  I don't find that explanation so convincing myself: your "curiosity" got you an unfair advantage in the grading of the assignment.  Your position that this advantage was not relevant to the final outcome is really not the point: many if not most students who cheat on assignments and exams could have reached the same outcome honestly if only they had been more patient (and honest!).  If you were really "just curious", you could have asked about it, and you certainly could have submitted only the allowed total number of submissions in a single day.

The real question is whether you deserve the punishment you've thus far been given, of a 0 on the entire assignment.  Generally, when students don't follow all the rules of an assignment, they can reasonably expect to be penalized for it in some way, but the penalty need not be the entire value of the assignment.  I think your position should be that you agree that you did not follow the rules and that you did this out of a combination of curiosity and stupidity.  You can make a reasonable case that you did not violate any fundamental principles of the assignment: all the work you turned in was your own, and you got it 100% correct well before the final deadline.  So all in all you did more good work than bad.  You did exhibit poor judgment and agree that some penalty is reasonable.  

I would suggest that you ask to be given the score that you got on the last attempt before you submitted on your friend's computer.  This score is undeniably legit, and giving you that score for the assignment seems like a nice compromise between giving no penalty for breaking the rules and ruining your entire course grade.

On the other hand, all this is to answer your question "Is this really a serious offense?"  (TL,DR: probably not too serious, but you did do something wrong.)  What I suggested above is really more a suggestion for what I think a just outcome of the faculty deliberation would be.  Depending upon how your system works, you may or may not have the opportunity to suggest a punishment.  As others have said, your real strategy here is to remain calm, explain all the facts as clearly as possible, accept that what you did is wrong and convey the impression that you are nevertheless a good student overall.  What they decide is really up to them.