A previous post transversal P (phase) gate shows that codes where all stabilizer elements have weights that are multiple of 4 will have a transversal $P$ gate. "Transversal" seems to have multiple definitions; here a gate $G$ is transversal for the code with stabilizer $S$ if it is in the normalizer of $S$ in the full unitary group : $G \in U_n : G' S G = S$. (note $G$ need not be in the clifford group). This is shown using $P^\dagger X P = \imath XZ, P^\dagger Z P = Z;$. At first guess I thought that codes where all stabilizer elements have weight that's a multiple of 8 would have a transversal $T$ gate. ($T^2=P$); but $T^\dagger X T = w_8 P Z X; T^\dagger Z T=Z$; where $w_8^8=1$. So it's not obvious if a similar argument can be used. Does anyone know how to extend the result for $P$ gate to $T$?