  We discuss twistor-like interpretation of the $Sp(8)$ invariant formulation
of 4d massless fields in ten dimensional Lagrangian Grassmannian $Sp(8)/P$
which is the generalized space-time in this framework. The correspondence space
$\mathbf{C}$ is $SpH(8)/PH$ where $SpH(8)$ is the semidirect product of $Sp(8)$
with Heisenberg group $\HG$ and $PH$ is some quasiparabolic subgroup of
$SpH(8)$. Spaces of functions on $Sp(8)/P$ and $SpH(8)/PH$ consist of $Q_P $
closed functions on $Sp(8)$ and $Q_{PH} $ closed functions on $SpH(8)$, where
$Q_P $ and $Q_{PH}$ are canonical BRST operators of $P$ and $PH$. The space of
functions on the generalized twistor space $\mathbf{T}$ identifies with the
$SpH(8)$ Fock module. Although $\mathbf{T}$ cannot be realized as a homogeneous
space, we find a nonstandard $SpH(8)$ invariant BRST operator $\QQ$ $(\QQ^2
=0)$ that gives rise to an appropriate class of functions via the condition
$\QQ f=0$ equivalent to the unfolded higher--spin equations. The proposed
construction is manifestly $Sp(8)$ invariant, globally defined and coordinate
independent. Its Minkowski analogue gives a version of twistor theory with both
types of chiral spinors treated on equal footing. The extensions to the higher
rank case with several Heisenberg groups and to the complex case are
considered. A relation with Riemann theta functions, that are $\QQ$-closed, is
discussed.
