gap> SolutionsMod2:=NullspaceModQ(TransposedMat(M),2);
[ [ 0, 0, 0, 0 ], [ 0, 0, 1, 1 ], [ 1, 1, 0, 0 ], [ 1, 1, 1, 1 ] ]

gap> SolutionsMod3:=NullspaceModQ(TransposedMat(M),3);
[ [ 0, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 0, 2 ], [ 0, 0, 1, 0 ],
  [ 0, 0, 1, 1 ], [ 0, 0, 1, 2 ], [ 0, 0, 2, 0 ], [ 0, 0, 2, 1 ],
  [ 0, 0, 2, 2 ] ]
