No $ [[3,1,2]] $ qubit code exists (more generally no $ ((3,2,2)) $ qubit code exists). See Why can't there be an error detecting code with fewer than 4 qubits?
However there does a exist a $ [[3,1,2]]_3 $ qutrit code with stabilizer generators $ XXX,ZZZ $.
Are there any other qutrit codes with no qubit analogues?
