I think if you find it in a chest you can pick it up. Otherwise you need the omnivore trait.
I found a bug:
View attachment 1098333
It is possible to bring Coconas parents heads when you escape the catacombs. But the hole to the catacombs and the graves will not trigger on the same night when you escape.
If you go to the grave yard the day after you CAN have the burial and seal the hole to the catacombs. But the new grave keeper will attack Cococna since she is still in her necromancer outfit.
IF you wait until Cocona gets her new clothes and then go to the graveyard, you can then seal the hole to the catacomb, but the burial of Coconas parents heads will NOT trigger.
So, now I have Coconas parents heads in my inventory. Forever. Since you can't toss them away.