How long are your cycles normally?
Some people get CM days before the ovulate, the day the ovulate, for a day or so after they ovulate...it would be helpful to know how long your cycles normally are. We'd have to assume a 14-ish day LP, but that would give us an idea.
Sperm can live 5-7 days, so CD9 might have a small chance, but CD 21 no.
If you did ovulate on CD15, the odds are low but slightly possible. According to this study, Day-specific probabilities of clinical pregnancy based on two studies with imperfect measures of ovulation You have about a 35-45% chance of pregnancy with intercourse the day before ovulation (as measured by an OPK or temp, not CM), that goes down to 20-30% 2 days before, etc etc (See figure 2).
I'm where you are at though, I think I had a big glob of CM on CD24, and we DTD on CD20 (late)....so I'm hopeful!