Consider an $ [\![n,k]\!] $ non-stabilizer code. The weight enumerator coefficients are 
$$
A_j:=\frac{1}{(2^k)^2} \sum_{p \in P_n,\,\mathrm{wt}(p)=j} |\mathrm{tr}(p \Pi)|^2
$$
where $ \Pi $ is the projector onto the code subspace.

Are the $ A_j $ always integers?

 
For stabilizer codes this is true see 
https://quantumcomputing.stackexchange.com/questions/30184/are-the-coefficients-of-the-weight-enumerator-polynomial-of-a-stabilizer-code-al/30187#30187

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?