Large Language Models (LLMs) have shown strong capabilities in code generation, but their adherence to fine-grained user intent with multiple constraints remains a significant challenge. Our empirical analysis reveals two key observations: 1) Model performance deteriorates quickly as the number of constraints in the user intent increases, and 2) While user intent does influence the model's logits, such an influence may not be strong enough to effectively steer the decoding process. To this end, we propose Intent-Amplified Code Generation (IntentCoding), a novel decoding strategy that enhances an LLM's ability to follow user intent. IntentCoding captures the influence of user intent by masking out the intent, and applies a multi-strength ensemble mechanism to amplify the effect of user intent during generation. IntentCoding is model-agnostic, requires no additional training, and integrates seamlessly with existing decoding procedures. To enable systematic evaluation, we also construct CodeConstraints, a benchmark dataset specifically designed to test user intent compliance under varying numbers of constraints. Experiments on our constructed Constraints, as well as popular IFEvalCode, HumanEval and LiveCodeBench datasets, show that our IntentCoding model significantly improves both constraint satisfaction and functional correctness compared to standard decoding approaches. IntentCoding achieves up to 71.0% relative improvement on CodeConstraints, achieves up to 67.3% relative improvement on IFEvalCode and achieves up to 29.3% relative improvement in pass@1 on HumanEval and LiveCodeBench compared with greedy decoding.