As far as I'm aware, the only ferries operating to Palma are from Barcelona, Valencia and Denia. The closest to CDA is Denia which is about 130 miles and then Valencia which is about 160 miles. However, I don't think the ferry from Denia (which takes five hours) takes cars, you'd have to go to Valencia for that. if you were thinking of doing that and taking a hire car on the ferry then I'd double check first as most hire companies do not allow their cars to be taken on ferries.
You can get quite a bit of info on this site www.aferry.co.uk
Regards, Julian