Herein, the design of linear dispersion codes for block based multiple-input multiple-output communication systems is investigated. The receiver as well as the transmitter are assumed to have perfect knowledge of the channel, and the receiver is assumed to employ maximum likelihood detection. We propose to use linear precoding and lattice invariant operations to transform the channel matrix into a lattice with large coding gain. With appropriate approximations, it is shown that this corresponds to selecting lattices with good sphere packing properties. Lattice invariant transformations are then used to minimize the power consumption. An algorithm for this power minimization is presented along with a lower bound on the optimization. Numerical results indicate that there is a potential gain of several dB by using the method compared to channel inversion with adaptive bit loading.