When someone says that they took "the moral high ground" (sometimes phrased as "the higher ground" or "the high road"), it involves a few things: 1. Some interaction between people (e.g., a dispute, an argument, an altercation, or some other problem). 2. The other person (or people) chose to do something that the speaker feels was wrong. 3. The speaker is saying that s/he did what was right in the situation. Example: "Sandra accused me of having an affair with her husband. She called me a few horrible names, right in the middle of the grocery store, and I really wanted to publicly humiliate her in return! If I were her husband, I'd be looking to ANYONE to be with besides her! But I chose to take the moral high ground: I simply told her she was mistaken, and walked away."

Wikipedia defines that the moral high ground, in ethical or political parlance, refers to the status of being respected for remaining moral, and adhering to and upholding a universally recognized standard of justice or goodness

If people take the moral high ground, they claim that their arguments, beliefs are morally superior to those being put forward by other people.

Maybe a morally (/ethically) high level (/high standard). No doubts possible.