For any prime power q we construct a nonlinear code consisting of 8 q codewords, each codeword having length 4 q, and with minimum distance 2( q − 1). When compared to a Hadamard code of the same size it is shown that the new code corrects at most one error less, irrespective of q. Hadamard codes, however, are not known to always exist, whereas the new codes exist always.