Consider an $ [\![n,k]\!] $ non-stabilizer code. Define the weight enumerator polynomial $ A(x) $ of the code as $$ A(x):=A_0+A_1x+\dots+A_nx^n $$
where $$ A_j:=\frac{1}{(2^k)^2} \sum_{p \in P_n,\,\mathrm{wt}(p)=j} |\mathrm{tr}(p \Pi)|^2. $$ Here $ \Pi $ is the projector onto the code subspace. For stabilizer codes the $ A_j $ are always integers see Are the coefficients of the weight enumerator polynomial of a stabilizer code always integers? . Is it the case that the $ A_j $ are always integers for non stabilizer codes as well?

If not, what is an example of a non-stabilizer code with $ A_j $ not integers?