We use a generalized Gray isometry in order to construct a previously unknown nonlinear (96,2/sup 36/,24) code as the image of a Z/sub 8/-linear Hensel lift of the binary Golay code. The union of this code with a relevant coset yields a (96,2/sup 37/,24) code. We show that this code and some of its shortenings are better than the best (non)linear binary codes known so far. For instance, the best earlier known code of length 96 and minimum distance 24 had 2/sup 88/ words.

Using tensor product constructions for the first-order generalized Reed-Muller codes, we extend the well-established concept of the Gray isometry between (Z/sub 4/, /spl delta//sub L/) and (Z/sub 2//sup 2/, /spl delta//sub H/) to the context of finite chain rings. Our approach covers previous results by Carlet (see ibid., vol.44, p.1543-7, 1998), Constantinescu (see Probl. Pered. Inform., vol.33, no.3, p.22-8, 1997 and Ph.D. dissertation, Tech. Univ. Munchen, Munchen, Germany, 1995), Nechaev et al. (see Proc. IEEE Int. Symp. Information Theory and its Applications, p.31-4, 1996) and overlaps with Heise et al. (see Proc. ACCT 6, Pskov, Russia, p.123-9, 1998) and Honold et al. (see Proc. ACCT 6, Pskov, Russia, p.135-41, 1998). Applying the Gray isometry on Z/sub 9/ we obtain a previously unknown nonlinear ternary (36, 3/sup 12/, 15) code.