Is there a way to publish my storyline file as an MP4?
There is no built-in option for MP4 publishing. This tread here discusses some workarounds: https://community.articulate.com/discussions/articulate-storyline/how-to-publish-in-mp4-format
Are you trying to publish the course as an MP4 for demonstration purposes? If so, the simplest solution would be to use Screenr (or Camtasia 8 if you have it) screen recording. You can record the course as though you were a learner and publish to MP4.
It looks like Cody and Michael have you covered here and I know that other users have shared their thoughts on publishing to a MP4 file or a video file as a feature request.