We develop a framework that exploits network coding (NC) and multiple-input/multiple-output (MIMO) techniques, jointly together, to improve throughput of downlink broadcast channels. Specifically, we consider a base station (BS) equipped with multiple transmit antennas that serves multiple mobile stations (MSs) simultaneously by generating multiple signal beams. Given the large number of MSs and the small number of transmit antennas, the BS must decide, at any transmission opportunity, which group of MSs it should transmit packets to, in order to maximize the overall throughput. We propose two algorithms for grouping MSs that take advantage of NC and the orthogonality of user channels to improve the overall throughput. Our results indicate that the proposed techniques increase the achievable throughput significantly, especially in highly lossy environments.