Scraf forgot all about this, so I'll put this here:
If you use a Black Writ of Challenge in the Battle Chateau, and if you fight the Furisode Girls there, they will have 2(if marchioness) audinos level 55, or 3(if duchess) audinos level 65. Just imagine having your Pokemon from a trade holding the lucky egg and having Exp. Power Level 3 on. That's a lot of experience points!