Network coding is a highly regarded technology for improving the capacity of wireless networks. COPE-sys network coding is an easily implemented and widely studied coding system. This paper studies the maximum throughput that can be supported by COPE-sys network coding over a practical CSMA/CA medium access control (MAC) protocol. Traditional method of analyzing capacity is multi-commodity flow (MCF) formulation, which assumes impractical centralized scheduling. We enhanced MCF formulation by taking into account the collision overhead in the distributed CSMA/CA protocol, to compute the maximum throughput. To the best of our knowledge, this paper is the first rigorous theoretical study of the achievable capacity over a multi-hop CSMA/CA based wireless network coding system.