  We construct weak (i.e. non-graded) modules over the vertex operator algebra
$M(1)^+$, which is the fixed-point subalgebra of the higher rank free bosonic
(Heisenberg) vertex operator algebra with respect to the $-1$ automorphism.
These weak modules are constructed from Whittaker modules for the higher rank
Heisenberg algebra. We prove that the modules are simple as weak modules over
$M(1)^+$ and calculate their Whittaker type when regarded as modules for the
Virasoro Lie algebra. Lastly, we show that any Whittaker module for the
Virasoro Lie algebra occurs in this way. These results are a higher rank
generalization of some results by Tanabe.
