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Large Language Models (LLMs) have revolutionized code generation but require significant resources and often over-generalize, limiting their task-specific efficiency. Fine-tuning smaller, open-source LLMs provides a cost-effective alternative. However, standard supervised approaches rely only on correct examples, missing valuable insights from failures. We introduce CodeLutra, a framework that leverages both correct and incorrect code attempts. Instead of using only correct solutions, CodeLutra applies iterative preference-based refinement, comparing successful and failed outputs to better approximate desired results. This approach narrows the performance gap with state-of-the-art larger models without requiring massive datasets or auxiliary models. For instance, on a challenging data science coding task, using only 500 samples improved Llama-3-8B's accuracy from 28.2% to 48.6%, approaching GPT-4's level. By learning from both successes and mistakes, CodeLutra provides a scalable and efficient path to high-quality code generation, making smaller open-source models more competitive with leading closed-source alternatives.