One approach to save memory would be pack the strings using a custom mapping (A => 0x00, C => 0x01, G => 0x10, T => 0x11). This will allow you to store 4 characters in an 8-bit byte, thus consuming 9 bytes instead of 34. You probably want to do this anyway even if you sort with an external utility, since you'll improve bandwidth efficiencies the longer you can maintain the data in this compressed format.

Sadly your lengths are just two characters too many to hold everything in a nice 64-bit quantity.