I'm not sure any random BA can help these days. Anecdotally at least, one of the recurring news stories about Millenials is about how so many can't get jobs with their BA degrees. OP is probably better off going to Lambda School or a similar technical boot camp.

This is just my personal experience. I've been successful in this industry for nearly a decade now, working my way up from junior to senior dev as a self taught programmer that dropped out of high school. It can absolutely be done. But that doesn't mean it ever helped me to have not had any academic achievements. I once held it as a point of pride to be able to make it without a degree. But I find it increasingly embarrassing as I get older and work almost exclusively with people that have those qualifications to not just have that piece of paper. The reality of life is that given identical skills and experience between two candidates, people are always going to choose the one with a degree. And justifying yourself at the higher levels of a career without one becomes increasingly untenable.

Anecdotally this is a popular idea, but it is surprisingly poorly supported by data. I did a deep dive on this a couple years ago, and there is actually little difference between early-career employment prospects for STEM and non-STEM bachelor degree holders.

I did not look at bachelors vs coding camp certificate.

I wonder how much of that is due to a big chunk of the STEM undergrad degrees (mainly science) being not so useful. Don’t think I’ve ever seen a scientist role requiring anything less than a PhD (at least nothing paying more then $40k a year) I find it hard to believe though, that the employment prospects for someone with an B.Eng. or B.S. CS are equally as bad for as someone with a B.A. in English or Psychology.

I think that's true for all schools below the top-10/top-20 (which covers the large majority of people, myself included).

For the elite schools, a STEM degree does confer advantage over non-STEM degrees.