python3 - <<'EOF'
import itertools
Cs=[[[1,1,0,1],[1,1,1,0],[0,1,0,1],[1,0,1,0]],[[1,1,1,0],[1,1,0,1],[1,0,0,1],[0,1,1,0]]]
def mm(Q):
 return tuple(tuple(sum(Q[i][k]*Q[j][k] for k in range(4))%2 for j in range(4)) for i in range(4))
allm=list(itertools.product([0,1],repeat=4))
def det(A):
 A=[list(r) for r in A]
 for c in range(4):
  p=next((r for r in range(c,4) if A[r][c]),None)
  if p is None:return 0
  A[c],A[p]=A[p],A[c]
  for r in range(c+1,4):
   if A[r][c]:A[r]=[x^y for x,y in zip(A[r],A[c])]
 return 1
Qs=[Q for Q in itertools.product(allm,repeat=4) if det(Q)]
for C in Cs:
 ct=sum(mm(Q)==tuple(tuple(r) for r in C) for Q in Qs)
 print('count Q',ct)
EOF