python3 - <<'EOF'
C=[[1,1,0,1],[1,1,1,0],[0,1,0,1],[1,0,1,0]]
import itertools
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
def inv(A):
 n=4
 M=[list(row)+[1 if i==j else 0 for j in range(n)] for i,row in enumerate(A)]
 for c in range(n):
  p=next((r for r in range(c,n) if M[r][c]),None)
  if p is None:return None
  M[c],M[p]=M[p],M[c]
  for r in range(n):
   if r!=c and M[r][c]:M[r]=[x^y for x,y in zip(M[r],M[c])]
 return [row[n:] for row in M]
for Q in itertools.product(allm,repeat=4):
 if not det(Q):continue
 if 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))==tuple(tuple(r) for r in C):
  R=inv(Q)
  print('Q',Q,'rowsums',[sum(r)%2 for r in Q],'Rrow',[sum(r)%2 for r in R],'R1',[sum(r[i] for r in R)%2 for i in range(4)])
  break
EOF