I think I could suggest a standard that would come close to making the case. Suppose we defined morality as conforming to a code of ethics that caused the least amount of harm to others?

Not a bad suggestion, but not all ethical/moral guidelines have anything to do with causing harm to others. For instance, it's honorable for a Palestinian to harm Jews (and himself, of course) with a suicide bombing. Their moral guidelines are just as real to them as mine are to me. I think you and I would both agree his are flawed, but from his perspective, and world-wide, I'd say the plurality opinion would be that taking human life, for any reason is wrong. So while your suggestion is good for most people, I don't think it "makes the case" that there is one absolute set of moral guidelines.