So do you want to also earn a degree in CS, or are you asking what you can do informally outside of your Physics degree to make you a good candidate for software jobs?
The CS classes in university are pretty specialized and different from other Engineering classes (let alone Physics classes). It's important IMO to at least take classes in Data Structures and Object Oriented Programming and other CS specific classes to make you better at architecting and coding software projects. I also found my class on Compiler Design to be very interesting and valuable, since understanding how compilers work has helped me a lot in working on the more complex software projects that I've worked on.
So if you want to also earn a CS degree, it would probably add at least a year or more to your university time. If you want to be considered for employment in some CS area, you would either need to learn all that stuff on your own (not easy), or choose a specific type of coding and the appropriate languages, and consider attending a "Coding Academy", which takes about 6 months of full time work, at least for those academies that we have here locally in Northern California.