Translating chart images into executable plotting scripts-referred to as the chart-to-code generation task-requires Multimodal Large Language Models (MLLMs) to perform fine-grained visual parsing, precise code synthesis, and robust cross-modal reasoning. However, this task is inherently under-constrained: multiple valid code implementations can produce the same visual chart, and evaluation must consider both code correctness and visual fidelity across diverse dimensions. This makes it difficult to learn accurate and generalizable mappings through standard supervised fine-tuning. To address these challenges, we propose a dual preference-guided refinement framework that combines a feedback-driven, dual-modality reward mechanism with iterative preference learning. Our approach introduces a structured variant generation strategy and a visual reward model to efficiently produce high-quality, aspect-aware preference pairs-making preference collection scalable and supervision more targeted. These preferences are used in an offline reinforcement learning setup to optimize the model toward multi-dimensional fidelity. Experimental results show that our framework significantly enhances the performance of general-purpose open-source MLLMs, enabling them to generate high-quality plotting code that rivals specialized chart-centric models and even some proprietary systems. The code and datasets are publicly available at https://github.com/Zhihan72/Chart2Code.