In this paper, we propose precoding methods for multiple input multiple output physical network coding systems, which employ the modulo operation. In our work, the transmit and receive filters are determined to maximize the minimum distance on the received constellations. Especially, to address non-concavity of the given problems, we change our problem into a concave one which can be optimized by an iterative method. Also, we propose a suboptimal non-iterative scheme whose performance is very close to the optimum iterative method. In our derivations, we prove that the modulo operation achieves the optimality in terms of the minimum distance. Finally, it is confirmed from the simulation results that the proposed systems outperform conventional schemes in terms of the error performance.