Establishing shared goals is a fundamental step in human-AI communication. However, ambiguities can lead to outputs that seem correct but fail to reflect the speaker's intent. In this paper, we explore this issue with a focus on the data visualization domain, where ambiguities in natural language impact the generation of code that visualizes data. The availability of multiple views on the contextual (e.g., the intended plot and the code rendering the plot) allows for a unique and comprehensive analysis of diverse ambiguity types. We develop a taxonomy of types of ambiguity that arise in this task and propose metrics to quantify them. Using Matplotlib problems from the DS-1000 dataset, we demonstrate that our ambiguity metrics better correlate with human annotations than uncertainty baselines. Our work also explores how multi-turn dialogue can reduce ambiguity, therefore, improve code accuracy by better matching user goals. We evaluate three pragmatic models to inform our dialogue strategies: Gricean Cooperativity, Discourse Representation Theory, and Questions under Discussion. A simulated user study reveals how pragmatic dialogues reduce ambiguity and enhance code accuracy, highlighting the value of multi-turn exchanges in code generation.