Your looking at a minimum of a 16' span, the only thing you can add lumber wise is 3 LVL beams and they will need to be 11 7/8 x 1 3/4 wide at a minimum.
There are a few other areas that you don't mention like how much height you have above the existing header, which way the gable runs, what loads are above this garage, just a roof or is there living space ?
I understand your desire to get ride of those pesky 8' doors (never understood why they did two small doors over one large one anyway) but you need to be very careful any undersizing of the new span header will cause serious and possibly dangerous problems.
Another option and probably your only real option to maintain height (7') is to add a steel " I " beam or perhaps a flitch beam (1/2" steel plate sandwiched between two pieces of lumber and bolted together).
Get back to us with the details above and we can look further.