|q⟩ Bad Qubits

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The 5-qubit perfect code is the [[5,1,d]][[5,1,d]] stabilizer code with cyclic generators XZZXIXZZXI, IXZZXIXZZX, XIXZZXIXZZ, ZXIXZZXIXZ. The distance dd is the smallest Pauli weight of an operator that commutes with all four generators (is in N(S)N(S)) but is not in the stabilizer group SS. What is dd?