There are a few qualities that theoretically make a character with LOG 13 possible, but of course such a character would have to be seriously minmaxed.
I won't bother doing the math right now, but there are, for example, exceptional attribute and metagenetic improvement (LOG) as qualities. Both raise the racial maximum by 1, and as such, the absolute maximum would be 12. There's probably something I'm forgetting, so 13 might not be too far fetched. Useful? Probably not so much.
Matrix in SR4 is not per sé broken. It's just a bit complicated and it takes some reading to get into.