What is an example of a code for which the Pauli group cannot be implemented transversally?
Mostly interested in an $ [[n,1,d]] $ code where $ d \geq 3 $.
Edit: By transversal I mean that there exists $ n $ single qubit operators $ g_1 \dots g_n $ such that the physical operator $ g_1 \otimes \dots \otimes g_n $ implements logical $ X $ (or $ Z $ or $ Y $ as the case may be). For example, in this sense every stabilizer code has a transversal implementation of the Pauli group (indeed in that case the $ g_i $ can all be picked to be Paulis).