Student understanding around measurement uncertainty is an important learning outcome in physics lab courses across the US, including at the University of Coloroado Boulder (CU), where it is among the major learning outcomes for the large introductory stand-alone physics lab course. One research tool for studying student understanding around measurement uncertainty, which we use in this course, is the Physics Measurement Questionnaire (PMQ), an open-response assessment for measuring student understanding of measurement uncertainty. Interpreting and analyzing PMQ data involves coding students' written explanations to open-response questions. However, the preexisting scoring scheme for the PMQ does not fully capture the breadth and depth of reasoning contained in our students' responses. Therefore, we created a new coding scheme for the PMQ based on responses from our students. Here, we document our process to develop a new coding scheme for the PMQ, and describe the resulting codes. We also present examples of what can be learned from applying the new coding scheme at our institution.