One of the most complex environment for the data transmission is the underwater channel. It suffers frequency selective deep fading with serious multi path time delay. The channel also has limited bandwidth. In this paper, the effect of Least Code Weight-Minimum Hamming Distance (LCW-MHD) polynomial code is studied using Viterbi Decoding Algorithm for the shallow Underwater Acoustic Communication (UAC) channel. Two different channels with the range of 100 and 1000 meters are considered for simulation purpose and the channel is designed using Ray Tracing algorithm. For data and image transmission in the channel, three different code rate of 1/2, 1/3 and 1/4 are considered and corresponding Bit Error Rate (BER) are evaluated. Result showed that the BER is least for the LCG-MHD polynomial code.