It's commonly agreed that the Island floats by itself, but when Ballos was imprisoned, his magic became a 'negative' energy on the Island and caused it to fall, and so Jenka created the Core, which countered Ballos, causing the Island to become neutral again. {And thus, rise again}
We can assume Jenka built the Core, or at least brought it to the Island, because of what the Gaudis say:
Code:
#0230
<PRI<MSGHave you ever seen the outside of
this island?<NOD<CLRThis island is floating high in
the skies.<NOD
As to how it manages to float...<NOD
That secret lies within this
maze.<NOD<END
Code:
#0200
<PRI<MSGLong, long ago, there lived a
witch on this island.<NOD
She's the one who constructed
this labyrinth, in order to
keep us Gaudis penned up.<NOD<END
The witch they're talking about would obviously be Jenka, who built the Labyrinth to protect the Core, because it's the only thing now keeping the Island afloat.