Both, yes and no!

Yes, designers should know something about technologies used by developers to bring designs to life.

No, designers should focus on psychology, improving user experience, selling, and other things that will make their designs better.

Designers and Developers need to work together. Combining both will give the best results. If there is a great collaboration between two, products, websites, etc. will be better and things will go smoothly.

Designer should know the limits of coding. Again, imagine holding a ball in your hands and you want to kick it longest possible. Knowing where to throw it (not too near or too far), so you can kick it out with your leg is very important. Same with design, knowing the limitations of coding can be useful in your design process. You don’t want to deliver an amazing looking design that will be badly executed.

To summarize, learn code good enough to understand limitations of it. Instead of going deep into code, go deep into psychology, selling, learning how to interview users, etc. and that way your designs will have the biggest impact.