Memory problem when solving a system of modular equations

FindInstance easily finds one solution, and fails to find two, so there might not be more:

FindInstance[{Mod[6 a + 0 b + 1 c + 1 d + 0 e + 1 f + 0 g + 1 h + 0 i,
       1235788] == 990685, 
    Mod[0 a + 3 b + 0 c + 0 d + 3 e + 0 f + 0 g + 0 h + 1 i, 
      1235788] == 404244, 
    Mod[4 a + 0 b + 0 c + 0 d + 0 e + 1 f + 1 g + 0 h + 0 i, 
      1235788] == 1228796, 
    Mod[1 a + 2 b + 1 c + 0 d + 1 e + 1 f + 1 g + 0 h + 0 i, 
      1235788] == 626461, 
    Mod[6 a + 0 b + 2 c + 0 d + 1 e + 1 f + 0 g + 0 h + 0 i, 
      1235788] == 814018, 
    Mod[4 a + 1 b + 1 c + 0 d + 1 e + 0 f + 0 g + 0 h + 1 i, 
      1235788] == 1052512, 
    Mod[1 a + 11 b + 0 c + 0 d + 0 e + 0 f + 0 g + 0 h + 0 i, 
      1235788] == 332360, 
    Mod[4 a + 2 b + 0 c + 2 d + 0 e + 0 f + 0 g + 0 h + 1 i, 
      1235788] == 417059, 
    Mod[7 a + 3 b + 1 c + 0 d + 0 e + 0 f + 1 g + 0 h + 0 i, 
      1235788] == 141258}, {a, b, c, d, e, f, g, h, i}, 
   Integers][[1]] // TableForm

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You can use the Modulus option for Reduce to get the general solution.

{ToRules[Reduce[{
   6 a + 0 b + 1 c + 1 d + 0 e + 1 f + 0 g + 1 h + 0 i == 990685, 
   0 a + 3 b + 0 c + 0 d + 3 e + 0 f + 0 g + 0 h + 1 i == 404244, 
   4 a + 0 b + 0 c + 0 d + 0 e + 1 f + 1 g + 0 h + 0 i == 1228796, 
   1 a + 2 b + 1 c + 0 d + 1 e + 1 f + 1 g + 0 h + 0 i == 626461, 
   6 a + 0 b + 2 c + 0 d + 1 e + 1 f + 0 g + 0 h + 0 i == 814018, 
   4 a + 1 b + 1 c + 0 d + 1 e + 0 f + 0 g + 0 h + 1 i == 1052512, 
   1 a + 11 b + 0 c + 0 d + 0 e + 0 f + 0 g + 0 h + 0 i == 332360, 
   4 a + 2 b + 0 c + 2 d + 0 e + 0 f + 0 g + 0 h + 1 i == 417059, 
   7 a + 3 b + 1 c + 0 d + 0 e + 0 f + 1 g + 0 h + 0 i == 141258},
{a, b, c, d, e, f, g, h, i}, Modulus -> 1235788]]}

The constant C[1] returned in the result may be set to any integer; however, there are only finitely many distinct solutions because of the modular arithmetic.