In this paper, a reconfigurable intelligent surface (RIS)-assisted full duplex communication for quadrature channel modulation (QCM) is proposed. The proposed scheme exploits transmit antennas and radio frequency mirror selection to transmit the real and imaginary parts of a QCM symbol independently to improve spectral efficiency. A dual polarized RIS is also employed to extend the indexing of receive antennas at a dual polarized half duplex receiver to separate the real and imaginary parts of the QCM symbol transmitted during downlink communication. This setup facilitates quadrature spatial modulation at the half duplex receiver and further enhances spectral efficiency. After transmit antenna selection, the remaining silent antennas at the base station are further harnessed to receive the QCM modulated uplink symbol from the half duplex transmitter unit. A decision-making method is adopted at the base station to find these silent antennas that receive uplink signals. Each antenna functions as either a transmit or a receive antenna with the help of a duplexer switch which assists in full duplex communication with minimal self-interference. Finally, an enhanced greedy detector is proposed to detect the signal with lower computational complexity. The system performance is evaluated using measures like average bit error rate, throughput, ergodic capacity, and energy efficiency, and compared with that of the existing state-of-the-art techniques.