In this letter, we introduce an analytical expression to the coded bit error rate (BER) of a MIMO system with a linear minimum mean square error (MMSE) receiver. We derive the moment generating function (MGF) of the SINR for arbitrary antenna configurations from the cumulative density function of SINR. We show that the moment generating function of the SINR at the MMSE detector output can be used to estimate the BER performance of a coded MIMO system. The analysis is simple and gives an accurate BER estimation at a high SNR. Based on the analytical and simulated results, the diversity order is dependent on the antenna configuration and the free distance of the convolutional code. Finally, we compare the analytical expression with simulated results for validation.