We propose Hierarchical Audio Codec (HAC), a unified neural speech codec that factorizes its bottleneck into three linguistic levels-acoustic, phonetic, and lexical-within a single model. HAC leverages two knowledge distillation objectives: one from a pre-trained speech encoder (HuBERT) for phoneme-level structure, and another from a text-based encoder (LaBSE) for lexical cues. Experiments on English and multilingual data show that HAC's factorized bottleneck yields disentangled token sets: one aligns with phonemes, while another captures word-level semantics. Quantitative evaluations confirm that HAC tokens preserve naturalness and provide interpretable linguistic information, outperforming single-level baselines in both disentanglement and reconstruction quality. These findings underscore HAC's potential as a unified discrete speech representation, bridging acoustic detail and lexical meaning for downstream speech generation and understanding tasks.