We propose a practical network code for the wireless two-way relay channel where all nodes communicate in full duplex (FD) mode. The physical layer network coding (PNC) operation is applied with the FD operating nodes, reducing the transmission time to a single time slot, hence doubling the spectral efficiency when compared to classical PNC systems. In our system model, binary phase shift keying modulated signals are transmitted over Rayleigh fading channels. We derive the theoretical error rates at relay and end nodes according to the maximum likelihood detection rule, in case of non-ideal self-interference cancellation. Theoretical results are also verified via simulations.