The Director of Graduate Studies for your department has made noises about "the professional turn," namely, writing for publication and not merely to demonstrate to the professor what you know. While you had a vague idea of what was meant, this is the first indication you have that you may be in the turn. What do you do now?
Your first stop is a meeting with your professor. Ask where it is likely to be publishable. And ask what else needs to be done to the paper to make it able to pass review.