It is from a video of the the YouTube channel TED-ed. Here it goes:
He galloped through his home in a frenzy, handling each item until it took on a lustrous sheen. Soon the palace heaved with gold.
I have cheched all the meanings of heave, but It seems to me none fit there.
The verb heave, when used intransitively as in the animation about Midas, means to rise up forming a mound, or to become swollen.
See here, for example.
One could also understand it figuratively as the palace swelled with gold as a river might swell with rain. You will sometimes see phrases like "the streets heaved with pedestrians" or "the wagon heaved with hay".
I too hear it as "heave". This is an odd use of the term, and possibly archaic from when the source the narrator is reading from was written.
My best guess is that it relates to the effort to move a heavy load, as if the palace was so full of gold that the walls were straining to contain it -- but this is not something I would use in any other context. Even taken metaphorically, it feels clumsy, as there are better verbs to evoke the same image.
