We propose a method for MIMO decoding when CSI is unknown to both the transmitter and receiver, which works when the underlying sources are drawn from a hypercubic space. Our proposed technique fits a minimum volume parallelepiped to the received samples. This problem can be expressed as a non-convex optimization problem that empirical results suggest can be solved with high probability by gradient descent. Our blind decoding algorithm can be used when communicating over unknown MIMO wireless channels using either BPSK or MPAM modulation. We apply our technique to jointly estimate MIMO channel gain matrices and decode the underlying transmissions with only knowledge of the transmitted constellation and without the use of pilot symbols. Empirical results show small sample size requirements, making this algorithm suitable for realistically encountered block-fading channels. Our approach has a loss of less than 3 dB compared to zero-forcing with perfect CSI, imposing a similar performance penalty as space-Time coding techniques with no loss of rate.