Code retrieval is vital to modern software engineering as it boosts reuse and speeds up debugging. However, current benchmarks primarily emphasize functional relevance while neglecting code quality. To address this gap, we introduce CoQuIR, the first large-scale, multilingual benchmark specifically designed to evaluate quality-aware code retrieval across four critical dimensions: correctness, efficiency, security, and maintainability. CoQuIR includes fine-grained quality annotations over 42,725 queries and 134,907 code snippets in 11 programming languages. Evaluating 23 retrievers (both open-source and proprietary) shows that even state-of-the-art models often fail to separate buggy or insecure code from robust counterparts. We further investigate methods for explicitly training retrievers to recognize code quality, demonstrating that quality-aware metrics can be improved without loss of semantic relevance; downstream code generation benefits from these gains. CoQuIR underscores the importance of embedding quality signals into retrieval systems as a crucial component for more trustworthy developer tools.