All stabilizer codes and also all non stabilizer codes that I am aware of, for example the ones here,
have a basis of codewords which are all uniform modulus superpositions of computational basis kets, in the sense that every nonzero coefficient has modulus $$ 1/\sqrt{|S|} $$ where $ |S| $ is the size of the support of the codeword.
In the particular case of stabilizer codes every nonzero coefficient has modulus $$ 1/\sqrt{2^r} $$ for some fixed $ r \leq n-k $. For a reference see https://quantumcomputing.stackexchange.com/a/27573/19675
What is an example of a (necessarily non-stabilizer) code for which the code space is not spanned by codewords which are all uniform modulus superpositions?
So to reiterate I'm looking for a $ d=2 $ code for which the code space is not spanned by codewords which are all uniform modulus superpositions.