An antenna coding approach for exploiting the spatial multiplexing capability of pixel antennas is proposed. This approach can leverage additional degrees of freedom in the beamspace domain to transmit more information streams. Pixel antennas are a general reconfigurable antenna design where a radiating structure with arbitrary shape and size can be discretized into sub-wavelength elements called pixels which are connected by radio frequency switches. By controlling the switch states, the pixel antenna topology can be flexibly adjusted so that the resulting radiation pattern can be reconfigured for beamspace spatial multiplexing. In this work, we introduce the antenna coder and pattern coder for pixel antennas, provide a multiple-input multiple-output (MIMO) communication system model with antenna coding in the beamspace domain, and derive the spectral efficiency. Utilizing the antenna coder, the radiation pattern of the pixel antenna is analyzed and efficient optimization algorithms are provided for antenna coding design. Numerical simulation results show that the proposed technique using pixel antennas can enhance spectral efficiency of 4-by-4 MIMO by up to 12 bits/s/Hz or equivalently reduce the required transmit power by up to 90% when compared to conventional MIMO, demonstrating the effectiveness of the antenna coding technique in spectral efficiency enhancement and its promise for future sixth generation (6G) wireless communication.