We consider sparse user detection in fading channels. With Rayleigh flat fading, deep fades occur with relatively high probability and it becomes challenging to provide highly reliable user detection, irrespective of the chosen multiuser detection algorithm. It has been proven that with a large number of receive antennas, this problem can be overcome and both the reliability and number of detectable users can be increased. In this paper, we show that similar improvements can be achieved by moderately increasing the number of transmit antennas at the user terminals. With multiple transmit antennas, code design becomes a problem. We provide a design criterion and show that the detection probability can be considerably improved by using the resulting well-balanced MIMO signature codes, especially in the high-reliability regime.