I'm assuming you're using QB64, in QBasic that would be a joke. If you DIM your array as integer, it will work:
DIM Array(38, 2048, 8192) AS INTEGER
The real question is, why would you need an array so HUGE!!! I'm sure there is a more memory-efficient way of accomplishing what you want. Working in QBasic, memory is a constant problem, and you must constantly look for other ways of doing things. The irony is, they usually turn out to be better ways.
P.S. As for details of memory methods and restrictions in QB64 you'd have to ask Galleon (QB64 forum?).