  We examine Penrose limits of the duality proposed by Guarino, Jafferis and
Varela between a type IIA massive background of the type of a warped, squashed
$AdS_4\times S^6$, and a 2+1 dimensional IR fixed point of ${\cal N}=8$ super
Yang-Mills deformed by Chern-Simons terms to ${\cal N}=2$ supersymmetry. One
type of Penrose limit for closed strings corresponds to a large charge closed
spin chain, and another, for open strings on giant graviton D-branes,
corresponds to an open spin chain on sub-determinant operators. For the first
limit, we find that like in the ABJM case, there are functions $f_a(\lambda)$
that interpolate between the perturbative and nonperturbative (string) regions
for the magnon energy. For the second, we are unable to match the gravity
result with the expected field theory result, making this model more
interesting than ones with more supersymmetry.
