We consider non-orthogonal space-time codes in multipath fading channels. For this, both minimizing the effect of the self-interference induced by the non-orthogonal code itself, and mitigating the inter-symbol-interference induced by the channel need to be addressed. We approach the problem by analyzing the example of rate one linear space-time transmissions from four transmit antennas. The starting point is the non-orthogonal ABBA-code minimizing the self-interference, which is one of the rate one quasiorthogonal codes for four antennas. In addition to applying time reversal on the part of a frame consisting of complex conjugated symbols, the non-orthogonal structure allows for multiple non-equivalent permutations of the transmission symbols. We observe that in addition to separating symbols and complex conjugated symbols, it is essential to interleave the symbols so that time epochs during which copies of the same symbols are transmitted, are far from each other.