In this paper, the problem of designing a linear precoder for Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, a novel and efficient methodology to evaluate the input-output mutual information for a general Multiple-Input Multiple-Output (MIMO) system as well as its corresponding gradients is presented, based on the Gauss-Hermite quadrature rule. Then, the method is exploited in a block coordinate gradient ascent optimization process to determine the globally optimal linear precoder with respect to the MIMO input-output mutual information for QAM systems with relatively moderate MIMO channel sizes. The proposed methodology is next applied in conjunction with the complexity-reducing per-group processing (PGP) technique, which is semi-optimal, to both perfect channel state information at the transmitter (CSIT) as well as statistical channel state information (SCSI) scenarios, with high transmitting and receiving antenna size, and for constellation size up to $M=64$. We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder, and the maximum diversity precoder for QAM with constellation sizes $M=16,~32$, and $~64$ and for MIMO channel size $100\times100$.