Using a certain 4-dimensional lattice, a new family of codes has been constructed that has a very low error rate. Two particular codes in this family appear to be excellent candidates for use in modems operating at 9. 6 and 14. 4 kb/s, respectively, on dial-up voice telephone lines. The new codes are trellis codes; the output of the encoder is a 4-tuple of odd integers that depends on the input data and the state of the encoder.