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.
-Bob
P.S. As for details of memory methods and restrictions in QB64 you'd have to ask Galleon (QB64 forum?).