My advice to you would be to improve (or acquire) your software engineering skills through practice, by doing real life projects. What I mean by that is pick an idea/project that excites you (e.g. An interactive website for non-philosophy majors to get a high level overview of philosophy) and do it (I know, "just do it" by itself it not so helpful).
Along the way, you'll probably hit many roadblocks (e.g. ruby? php? html? ftp? git? heroku? aws?) but overcoming them through research, trial and error will teach you a lot about software engineering and you'll come out of the experience more educated. There's also an added benefit of building up a portfolio that shows you care more about solving problems (remember, we started from an idea) than a specific set of technologies (only a tool to execute on said idea).
When you think you're "good enough" to provide value to a company, I would start applying to job openings in parallel. Good luck! I'm actually a mechanical engineer by education, but transitioned to software after graduating using the method described above.