python3 - <<'EOF'
import itertools
def det(A):
 n=len(A)
 A=[list(r) for r in A]
 for c in range(n):
  p=next((r for r in range(c,n) 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,n):
   if A[r][c]:A[r]=[x^y for x,y in zip(A[r],A[c])]
 return 1
pairs=[(i,j) for i in range(6) for j in range(i+1,6)]
cnt=0
for bits in itertools.product([0,1],repeat=15):
 A=[[0]*6 for _ in range(6)]
 for (i,j),b in zip(pairs,bits):A[i][j]=A[j][i]=b
 cnt+=det(A)
print(cnt)
EOF