This depends on how you define morality and how you define character.
If you define morality as acting for the right reasons, then you would need a good character in order to act morally. But if morality simply consists of doing the right thing, then an excellent character is not needed. I could well do good things out of greed or pride. Then, I would have a poor (to my mind) character but would be acting morally.
Similarly, do I have to want to act morally in order to have an excellent character? If so, then I would need an excellent character in order to act morally. But what if I don't want to act morally but I do so anyway? Does that mean I have a bad character because I want to act in bad ways? If so, I could act morally without having a good character.