Yes, you can use a Student license for your course requirements for any undergraduate degree, or Masters, or PhD.
You can publish / post any of your code that you create for your coursework (including a thesis) for free access.
You cannot use the Student license to publish research papers -- not unless publishing a paper is a requirement of your degree. Publishing research papers is permitted with an Academic license, however.
If there should ever come a time when a company was interested in hiring you to develop your MATLAB code more, or buying code you developed with a student license, then you would need to get a commercial / professional license.
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