Original manuscript July 29, 2009We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear error-correcting codes for classical asymmetric channels, with which we systematically construct quantum amplitude damping codes with parameters better than any prior construction known for any block length n ≥ 8 except n=2r-1. We generalize this construction to employ classical codes over GF(3) with which we numerically obtain better performing codes up to length 14. Because the resulting codes are of the codeword stabilized (CWS) type, conceptually simple (though potentially computationally expensive) encoding and decoding circuits are available.