What exactly do computer software engineers do?

I’m planning to be a computer software engineer when I grow up. What do they do? Do they just stay at home and make software, then sell them or do they apply for a company that makes software?

I also want to be a graphics designer, but I’m not sure if I can do both. Is it possible to do both? If it is, what classes should I take in high school?

They write computer code.