Recent designs for space-time block codes (STBCs) have exploited the structure of the codes (unitary, orthogonal) to enable systematic construction. Code sets found by an exhaustive search to optimize cost functions can often achieve performance gains of several dB; however, such searches are not feasible for large block or constellation sizes. By exploiting isometries between codewords, properties of the searched codes are determined which suggest a systematic code construction method. The results are nonlinear hierarchical codes (NHCs), where coding gain is optimized at each layer of the hierarchy and codes of arbitrary block-sizes/constellations can be designed. A fundamental difference between the structured codes (unitary, orthogonal) and NHCs is that in NHCs, the relationship between codewords is manipulated, rather than properties of the individual codeword. The proposed scheme is essentially a generalization of D. Slepian's group codes for the Gaussian channel (see Bell System Tech. J., vol.47, p.575-602, 1968) to the multiple-input multiple-output quasi-static fading channel.