[MalcolmDiggs]

It depends on how you define 'code'.

Should the CTO be given a chunk of the backlog to complete for this sprint? No, that's probably not a good use of their time.

Should the CTO lend a hand when the team gets stuck and have an active role in code reviews? Certainly! That seems well within the scope of their duties.

I think part of being a technical leader for a company is getting your hands dirty when your experience/insight could save the team significant time/headache. Coding for coding's sake isn't advisable, but coding as a teaching/mentoring tool could be very valuable for the members of your team.