In recent years, researchers have proposed numerous benchmarks to evaluate the impressive coding capabilities of large language models (LLMs). However, current benchmarks primarily assess the accuracy of LLM-generated code, while neglecting other critical dimensions that also significantly impact code quality in real-world development. Moreover, relying exclusively on correctness as the guiding metric renders LLMs susceptible to data contamination. Therefore, this paper proposes the RACE benchmark, which comprehensively evaluates the quality of code generated by LLMs across 4 dimensions: Readability, mAintainability, Correctness, and Efficiency. Specifically, considering the demand-dependent nature of dimensions beyond correctness, we design various types of user requirements for each dimension to assess the model's ability to generate correct code that also meets user demands. We analyze 28 representative LLMs based on RACE and find that: 1) current correctness-centric benchmarks fail to capture the multifaceted requirements of code in real-world scenarios, while RACE provides a comprehensive evaluation that reveals the defects of LLMs across multiple dimensions; 2) the RACE benchmark serves as an effective tool for resisting the risk of data contamination; 3) even the most advanced code LLMs still encounter significant challenges in customized requirements involving complex instructions; 4) most LLMs exhibit an inherent preference for specific coding style. These findings highlight the need for a multidimensional evaluation of code LLMs, emphasizing metrics beyond correctness for real-world applications. Future efforts should aim to develop novel learning algorithms to enhance code generation under varied constraints and improve coverage and usability for diverse user needs.