A coset of a convolutional code may be used to generate a zero-run length limited trellis code for a 1-D partial-response channel. The free squared Euclidean distance, dfree2, at the channel output is lower bounded by the free Hamming distance of the convolutional code. The lower bound suggests the use of a convolutional code with maximal free Hamming distance, dmax(R,N), for given rate R and number of decoder states N. In this paper we present cosets of convolutional codes that generate trellis codes with dfree 2>dmax(R,N) for rates 1/5⩽R⩽7/9 and (d free2=dmax(R,N) for R=13/16,29/32,61/64, The tabulated convolutional codes with R⩽7/9 were not optimized for Hamming distance. Instead, a computer search was used to determine cosets of convolutional codes that exploit the memory of the 1-D channel to increase dfree2 at the channel output. The search was limited by only considering cosets with certain structural properties. The R⩾13/16 codes were obtained using a new construction technique for convolutional codes with free Hamming distance 4. Newly developed bounds on the maximum zero-run lengths of cosets were used to ensure a short maximum run length at the 1-D channel output