solve_mod is horribly slow for linear systems

[zimmerma]

consider the following with Sage 4.8:

sage: s
[69*a + b + 76*c == 59, 43*a + b + 5*c == 91, 69*a + b + 76*c == 42, 70*a + b + 26*c == 98, 65*a + b + 28*c == 65, 66*a + b + 60*c == 106, 84*a + b + 93*c == 1]
sage: time sol = solve_mod(s, 107)
Time: CPU 190.52 s, Wall: 366.98 s

I know the documentation of solve_mod says it uses exhaustive enumeration for small primes, however it would be easy to recognize linear systems and call corresponding routines for them.