Friedrich Nietzsche often uses the word "morality" in a pejorative sense, but sometimes uses it for a system of values that he is promoting himself, a re-valued system of values. This causes some confusion.
Accordingly, the online Stanford Encyclopedia of Philosophy uses the initials MPS, for "morality in a pejorative sense" in an article on Nietzschean themes in moral and political philosophy.
What Nietzsche despised about MPS boils down to three presumptions: that human beings are free and so morally responsible for our actions; that the human self is transparent, so some of us can make coherent judgment about why others have acted as they have; and that human selves are sufficiently similar for it to be possible to announce a single moral code for all.
Nietzsche targets the first of these, for example, when he writes in Beyond Good and Evil that "the concept of a causa sui is something fundamentally absurd," and that MPS requires that absurdity; the ability "to pull oneself up into existence by the hair, out of the swamps of nothingness."
As to transparency, FN writes in Daybreak, "We have expended so much labor on learning that external things are not as they appear to us to be -- very well! the case is the same with the inner world!"
Finally, as to human commonality: quoting BGE again, when one hears a moral imperative from any one, "the question is always who he is, and who the other person is."
In particular, of course, for Nietzsche the distinction must be made between ordinary folk and the "highest type," the ubermensch.
I've just been paraphrasing the SEP article mentioned above. I hope to have some more personal commentary about this material for you tomorrow.