In this paper, we propose an energy-efficient solution for implementing Network Coding (NC) in wireless networks based on the IEEE 802.11 Standard. The proposed mechanism, called GreenCode, allows nodes to duty cycle by switching to a low-power (sleep) state when they overhear coded packet transmissions that will not provide any new information for them. To facilitate the sleep operation, bidirectional transmissions involving both coded and non-coded packets between pairs of sender-receiver nodes are integrated into the operation of GreenCode. Both analytical and simulation results presented in this paper show the high energy efficiency of GreenCode with gains of up to 360% when compared to the existing mechanisms based on the IEEE 802.11 Standard.