Harvesting energy from radio frequency signals along with transmitting data through them is appealing for different wireless communication scenarios such as RFID systems and implantable devices. In this paper, we propose a technique to design nonlinear codes for use in such systems taking into account both energy transmission and error rate requirements. Specifically, we propose using concatenation of a nonlinear trellis code with an outer low density parity check code. Via examples, we observe that our designed codes operate at SNRs 2.4dB away from information theoretic limits, and they outperform reference schemes of concatenating LDPC codes with nonlinear memoryless mappers and using classical linear block codes in a time switching mode. We note that it is possible to close the gap to the information theoretic limits further by more sophisticated receiver designs and more complex encoders.