Widely used codes, such as turbo and LDPC codes, have very low block error rates at very high block lengths, making them suitable for coherent communications where the channel state information is available at the receiver. In the new age of ultra-low latency communications, the performance of error-correcting codes at short block lengths has become critically important. Sparse Regression Codes (SPARCs), bridging sparse signal recovery and error control coding, emerge as a promising alternative for noncoherent channels. The existing literature has shown that SPARCs are capacity-achieving on the AWGN channel at asymptotic block lengths using an AMP decoder. In our work, we extend the study of very short-length SPARCs for unknown fading channels. We introduce a novel non-coherent detector utilising multiple antennas at the receiver without the channel state information. Specifically, we develop a new greedy algorithm, leveraging the channel statistics, known as the maximum likelihood matching pursuit (MLMP). Our simulation results show that MLMP boasts a significant block error performance gain over the traditional Block-Orthogonal matching pursuit (Block-OMP) with reduced computational demands.