> How do human groups glorifying immorality imply that there is no universal moral code? If the universal moral code exists outside of those groups, then it can be applied to their actions, and we can call them wrong for the thing they glorify.

Those groups would also call us wrong. If groups of humans tend to display very different and incompatible moral codes, that's a strong argument against a universal morality. Another argument against it is that most people in groups that glorified what terrifies us lived and died without showing an ounce of remorse for their actions.

> Your very sentence implies a universal moral code. You are calling murder, slavery, and genocide wrong.

Not at all. I used those examples because I know that most contemporary readers would agree. The fact that there is no universal moral code does not mean we can't have a moral code.