Full disclosure, I have not been diagnosed with ASPD officially. According to the Levenson Psychopathy Scale, I scored higher than 77% of people taking the test for primary psychopathic traits and 91% higher for secondary psychopathic traits. I was a bit surprised, but only due to various people always insisting what a good person I am because they don't know any better.

Anyway, I do have a pretty strong moral code. Mine is built on utilitarianism. I did not intentionally set out to make it so, I just learned in an ethics class about various moral philosophies and recognized that I work from a utilitarian perspective. The caveat is that there are certain areas where I hold a double standard - I may view something as morally wrong, but only when others do it. Or perhaps it's more accurate to say I just don't care if I do certain things which I consider to be "wrong." However, I think that's how most people are, I'm just more self aware about my own hypocrisy. My lack of empathy makes the double standard feel acceptable to me. But those are the exceptions and not the rule. I don't just throw morals by the wayside if they're inconvenient, either. I don't eat animals due to my moral beliefs, and that is often inconvenient.

ETA - I am an atheist as well and I disagree that atheists have no basis for a moral code. Deontological morals are but one philosophy.