> with(linalg):
> with(ListTools):

> A:= matrix(25,4,[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1],
> [1,1,0,0],[1,-1,0,0],[1,0,1,0],[1,0,-1,0],[1,0,0,1],[1,0,0,-1],
> [0,1,1,0],[0,1,-1,0],[0,1,0,1],[0,1,0,-1],[0,0,1,1],[0,0,1,-1],
> [1/2,1/2,1/2,1/2],[1/2,1/2,1/2,-1/2],[1/2,1/2,-1/2,1/2],
> [1/2,1/2,-1/2,-1/2],[1/2,-1/2,1/2,1/2],[1/2,-1/2,1/2,-1/2],
> [1/2,-1/2,-1/2,1/2],[1/2,-1/2,-1/2,-1/2],[0,0,0,0]]);

> Count:= 0;
> f:= proc(x)
> 	if irem(C[x,1],12)=0 then x;
> 	else 25;
> 	end if;
> end proc:

> for a from 0 to 11 do
> for b from 0 to 11 do
> for c from 0 to 11 do
> for d from 0 to 11 do
> e1:= a+2*b+3*c+2*d: e2:= a+b+c: e3:= b+c: e4:= c:
> B:= matrix(4,1,[[e1],[e2],[e3],[e4]]):
> C:= multiply(A,B):
> S:= seq(f(i),i=1..25):
> L:= MakeUnique([S]):
> M:= submatrix(A,L,[1,2,3,4]):
> if rank(M)=4 then Count:=Count+1;
> print(a,b,c,d) end if:
> end do; end do; end do; end do;
> 
> Count;