In Discrete Variable Quantum Key Distribution (DV-QKD), the homodyne detection method is frequently employed for its simplicity in use, effectiveness in terms of error correction, and suitability with contemporary optical communication systems. Being a coherent detection method, it relies on a local oscillator whose frequency is matched to that of the transmitted carrier's signal. In this paper, we evaluate a Free Space Optical (FSO) DV-QKD system based on the KMB09 protocol using Homodyne detection under random phase fluctuation and depolarizing noise error. We present simulation results for System Efficiency and Quantum Bit Error Rate (QBER) for the proposed model. An obtained efficiency ({$25\%$}) for our proposed DV-QKD system model shows that under atmospheric turbulence and noise effect and it is in line with the available analytical results. However, the inclusion of random phase fluctuation and noise led to higher-than-normal QBER which is anticipated in a real-world scenario.