See, to be honest, no matter how much qualified you are, you will face many difficulties in getting a coding or computer related job with an arts degree with you. If you are sure to make a living with coding, then I would highly suggest you to go for a degree that matches your goals. If you have the capacity, then please go for an engineering course for a B.Tech or a BE degree. But if you don't want to do your bachelors again, then you may also go for a masters degree in Computers, but for that you'll have to teach yourself some of the concepts, which can be pretty hard. Consider both options, and then make an informed decision.

Hope I have answered your question. All the best!