This paper proposes an XOR physical layer network coding (XOR-PLNC) with non-linear precoding for quadrature amplitude modulations (QAMs) in bi-directional MIMO relay systems. The proposed XOR-PLNC applies power loading in order to improve the transmission performance. The proposed XOR-PLNC introduces a modulus adapted to channel gains. Moreover, the modulus is further reduced in cooperation with modulo operation which the non-linear precoding employs for improvement of transmission power efficiency. The use of the reduced modulus improves the energy efficiency of the signal transmission, which improves the transmission performance in the proposed XOR-PLNC. The performance is evaluated by computer simulations in bi-directional MIMO relay channels with 16QAM to 1024QAM.