A CWS code can be defined in terms of stabilizer codes/stabilizer states and graph states. See What is an example of a non-additive code that is not a CWS code?
Is the $ ((11,2,3)) $ nonadditive quantum error-correcting code given in On the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes a codeword stabilized code?
Certainly all the coefficients are $ \pm 1 $ up to a global scalar (in fact all the nonzero coefficients are $ +1 $) so that necessary condition is met.
Maybe there is some way of confirming this (or deriving a contradiction) by think about what graph that $ ((11,2,3)) $ code would have to correspond to?