Many well known stabilizer codes are $ GF(4) $ linear. For example, the perfect $ [[5,1,3]] $ code and the $ [[7,1,3]] $ Steane code are both $ GF(4) $ linear.
The $ [[9,1,3]] $ Shor code is not $ GF(4) $ linear since it is a CSS code with the number of $ X $ type stabilizer generators different from the number of $ Z $ type stabilizer generators.
Is there some way to modify the Shor code to get a $ GF(4) $ linear $ [[9,1,3]] $ code?
More generally, what is an example of a $ GF(4) $ linear $ [[9,1,3]] $ code?