Go only as far in depth as is necessary. For example, a diagnosis of insomnia should be included. Your roommates loud snoring should not.
There is a difference between providing explanations and making excuses. A loudly snoring roommate is an excuse. A diagnosis of insomnia is an explanation.
If it were me, I'd tell the story by spinning it as positively as possible.
1. Academic warning
2. Sought medical help and was diagnosed with insomnia and given a prescription
3. grades improved through hard work and laser-like focus
End of story.
The C&F element to the bar, as I understand it, is less about what mistakes you've made and more about being upfront and honest about them. I think people spend far too much time worrying about explaining why things happen instead of simply saying what happened, what you did to rectify the situation, and what the result has been.
I have a buddy who was popped for misdemeanor possession of marijuana while in college. He was upfront about it and didn't make excuses, saying it was a lapse in judgment borne out of immaturity that he learned from. He not only got into law school (and did well), but is now a practicing attorney. Academic warning, in my opinion, does not rise to the same level as misdemeanor possession of a narcotic.
Plus, you can amend your C&F answers while in law school, usually with the help of a faculty member....