@Shakur
She doesn't have a core that flesh golems usually have neither she is a being artificially made that the homunculus are so neither words should be used for them.
Well, first off I have not read the novel so I don´t know if she has one or not.
But regardless it doesn't really matter, it's true that most golems have cores nowadays, but originally that was not the chase and there is nothing that says a golem MUST have a core.
The original golem was made from clay and animated by the "words of God" (so pretty much holy power and not a core) by writing the word "truth" on its forehead. ( or sometimes chest )
This was also its weakness as if you removed parts of the word it killed the golem, and the core is usually the weakness of the golems in pop culture when they don´t have the words on them.
Honestly, I have been trying to find out where the "golem core" concept comes from but I have not managed to find a source for it.
It's only in recent times where golems have been given cores, likely too avoid the religious connection towards a more magical one... but again I don´t know where it's from.
TLR
Golem cores have for sure become a big part of the golem lore, but it's not always necessary for a golem to have one.