In this paper, we investigate a robust joint precoder-decoder design scheme for a multiple-input multiple-output (MIMO) physical layer network coding (PNC) based two-way relay system. Precoders at the source nodes and decoder at the relay node are used to facilitate PNC operations during multiple access stage. Both channel estimation error and antenna correlations are used to formulate an optimization problem to minimize weighted mean square error (WMSE) under a total power constraint. The problem becomes non- convex, and we propose an algorithm to solve it optimally. The effect of estimation error, antenna correlation parameters, weighting parameters, and number of antennas at nodes are also considered in the numerical analysis.