Automatic ICD coding from clinical text is a critical task in medical NLP but remains hindered by the extreme long-tail distribution of diagnostic codes. Thousands of rare and zero-shot ICD codes are severely underrepresented in datasets like MIMIC-III, leading to low macro-F1 scores. In this work, we propose a data-centric framework that generates high-quality synthetic discharge summaries to mitigate this imbalance. Our method constructs realistic multi-label code sets anchored on rare codes by leveraging real-world co-occurrence patterns, ICD descriptions, synonyms, taxonomy, and similar clinical notes. Using these structured prompts, we generate 90,000 synthetic notes covering 7,902 ICD codes, significantly expanding the training distribution. We fine-tune two state-of-the-art transformer-based models, PLM-ICD and GKI-ICD, on both the original and extended datasets. Experiments show that our approach modestly improves macro-F1 while maintaining strong micro-F1, outperforming prior SOTA. While the gain may seem marginal relative to the computational cost, our results demonstrate that carefully crafted synthetic data can enhance equity in long-tail ICD code prediction.