A code is a non-stabilizer code if it is not equivalent by local unitaries to a stabilizer code.
What is an example of a non-stabilizer code with distance $ d \geq 2 $?
Are there any non-stabilizer codes that are known to have especially good properties, for example better parameters than any known stabilizer code?
If you have a code in mind that seems like it is non-stabilizer then feel free to share! (even if you don't have a proof that it's not equivalent to a stabilizer code by local unitaries, I'm mostly just interested in seeing code constructions that seem essentially different from stabilizer codes).