Regarded as one of the future enabling technologies of the Internet of Things at the biological and nanoscale domains, Molecular Communication (MC) promises to enable applications in healthcare, environmental protection, and bioremediation, amongst others. Since MC is directly inspired by communication processes in biological cells, the engineering of biological circuits through cells' genetic code manipulation, which enables access to the cells' information processing abilities, is a candidate technology for the future realization of MC components. In this paper, inspired by previous research on channel coding schemes for MC and biological circuits for cell communications, a joint encoder and modulator design is proposed for the transmission of cellular information through signaling molecules. In particular, the information encoding and modulation are based on a binary parity check scheme, and they are implemented by interconnecting biological circuit components based on gene expression and mass action reactions. Each component is mathematically modeled and tuned according to the desired output. The implementation of the biological circuit in a simulation environment is then presented along with the corresponding numerical results, which validate the proposed design by showing agreement with an ideal encoding and modulator scheme.