If by design you mean UI/UX, then you can definitely pick it up yourself if you are really passionate about it. Helps in understanding software design later on.

I have a friend, we studied IT together, near the end of the course, he found out he like UX and he transitioned into that while working in a company.

I have another colleague, picked up programming all by himself without a diploma and a degree and is higher paid than me.

Just goes to show, if you want something badly enough, you will go through a lot to get it regardless of a degree.

If your idea of design is not IT related, then you might have to go to some classes, try out something to see if it is just a hobby or something you want to do as a job.

by the way, im not discouraging you to be a designer but it could be pretty tough.
Software engineer seems like a pretty good course if you're the type of person who enjoy executing task logically, money's not bad too when u go into industry full time..

just to let you know that you can also keep design as a hobby or interest, while pursue software engineering full time, who knows one day you could combine both