The linear closed-loop MIMO precoding technique employs the channel state information at both sides of the link to optimize various criteria such as the capacity, the mean square error, the mutual information. However, the cost is generally an increased complexity and the theoretical study of such a system can be difficult, i.e. obtain criteria such as the Bit Error Rate or Logarithm of Likelihood Ratio (LLR). Some studies are available for diagonal form precoders, but it is often difficult to deal with a precoder that chooses between different forms to adapt to the channel state, as in the case for the max-dmin precoder. In this paper, we propose a new approximation of the mutual information (MI) which is expressed as a function of the minimal distance. Indeed, our recent works permit us to obtain the probability density function of the minimal distance, and, this is the main point, to deal with the multi-forms. The MI can then be averaged over the statistics of the channel and the result is available for any MIMO system and any modulation size for the example of max-dmin.