Instead of the complicated Steane code, I don't understand why don't we use a much simpler and exact imitation of the classical Hamming code.
So here is my idea: Let's have 7 qubits, and we will encode our qubit in the last wire. Based on this we will create CNOTs gates which will fix the parity of the code. The control would be qubit 1, 2, 4 just like classical code. This is all exactly like classical code.
Then to decode it, you can create 3 ancillas which simply read/copy the values of 1, 2, 4 qubits. So for now, just like classical qubits, you have the value specified in the three ancillas indicating where the error is.
All that remains to be done is performing a partial measurement of the three ancillas to just get the index of the error. The rest is unchanged.
So what's the problem with this? What is the point of creating categories of even codes and odd ones and collapsing into them like in Steane code?