ICD(International Classification of Diseases) coding involves assigning ICD codes to patients visit based on their medical notes. ICD coding is a challenging multilabel text classification problem due to noisy medical document inputs. Recent advancements in automated ICD coding have enhanced performance by integrating additional data and knowledge bases with the encoding of medical notes and codes. However, most of them ignore the code hierarchy, leading to improper code assignments. To address these problems, we propose a novel method based on associated and hierarchical code description distillation (AHDD) for better code representation learning and avoidance of improper code assignment. We utilize the code description and the hierarchical structure inherent to the ICD codes. Therefore, in this paper, we leverage the code description and the hierarchical structure inherent to the ICD codes. The code description is also applied to aware the attention layer and output layer. Experimental results on the benchmark dataset show the superiority of the proposed method over several state-of-the-art baselines.