A bit-interleaved coded modulation (BICM) scheme with iterative (soft) demapping and decoding (IDD) is developed for non-coherent communication over a multipleinput multiple-output (MIMO) channel. The scheme exploits the underlying Grassmannian geometry of the signalling scheme that approaches the ergodic capacity of the noncoherent model at high signal-to-noise ratios. This geometry guides the construction of the MIMO constellation and gives rise to a computationally-efficient list-based demapping algorithm. The incorporation of a scheme that enables the decoder to augment the demapping list virtually eliminates the mild performance degradation of the efficient demapper. Simulation results demonstrate that at high data rates the proposed scheme can provide significantly better performance than several training-based BICM-IDD schemes.