The eleventh quest is given to you by Mother Dearest: find the lance of Longinus from among all the other lances kept in the vault.
We're looking for a lance head in the shape of a spear, is made of copper and engraved with a fish symbol. Out of the (at least) twelve possibilities, this can be found quickly by going right when entering the catacombs and proceeding directly to the back of the room. It is third from the right.
Examining all the tombs in the catacombs unlocks Cataphile Trait (+1 Erudition). Leave the catacombs to finish the chapter.