Guest on Elucidations is Brian Leiter (audio), who makes quite the effort to explain Nietzsche and clarify the various meanings morality in this context receives. In Nietzsche, next to a morality in the pejorative sense, which Nietzsche opposes, there is also some elate morality, that is different and not negative in Nietzsche's view. And so, it is important to get the pejorative morality clear. In Leiter's view, Nietzsche was very much against Utilitarianism and against the morality in Kant.
After the interview, I am not sure whether Leiter's interpretation of Nietzsche would be agreed upon by most authoritative readings of his work and I am far from being able to assess that, but Leiter does seem to emphasize that this interpretation is especially his. No matter what, Nietzsche's importance, so it seems to me, remains that he attacks the assumption of self-evidence in morality and forces us to think even the most obvious moral truisms through.