Inspired by the brain's information processing using binary spikes, spiking neural networks (SNNs) offer significant reductions in energy consumption and are more adept at incorporating multi-scale biological characteristics. In SNNs, spiking neurons serve as the fundamental information processing units. However, in most models, these neurons are typically simplified, focusing primarily on the leaky integrate-and-fire (LIF) point neuron model while neglecting the structural properties of biological neurons. This simplification hampers the computational and learning capabilities of SNNs. In this paper, we propose a brain-inspired deep distributional reinforcement learning algorithm based on SNNs, which integrates a bio-inspired multi-compartment neuron (MCN) model with a population coding approach. The proposed MCN model simulates the structure and function of apical dendritic, basal dendritic, and somatic compartments, achieving computational power comparable to that of biological neurons. Additionally, we introduce an implicit fractional embedding method based on population coding of spiking neurons. We evaluated our model on Atari games, and the experimental results demonstrate that it surpasses the vanilla FQF model, which utilizes traditional artificial neural networks (ANNs), as well as the Spiking-FQF models that are based on ANN-to-SNN conversion methods. Ablation studies further reveal that the proposed multi-compartment neuron model and the quantile fraction implicit population spike representation significantly enhance the performance of MCS-FQF while also reducing power consumption.