The O(S^4) asymptotics are harsh.
I can run 8 copies at 64x64 without running out of memory, 4 copies at 80x80, and conjecture only 1 copy at 112x112.
If I used single precision floating point instead of double precision, or paged out half of the data (accessed infrequently) to disk, I would be able to run 1 copy at 134x134. But I don't know if there is a version of GSL that supports single precision.
If I did both, I could run 1 copy at 160x160, which is getting into the realm of interesting sizes...