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We discuss twistor-like interpretation of the $Sp(8)$ invariant formulationof 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 offunctions on the generalized twistor space $\mathbf{T}$ identifies with the$SpH(8)$ Fock module. Although $\mathbf{T}$ cannot be realized as a homogeneousspace, 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 proposedconstruction is manifestly $Sp(8)$ invariant, globally defined and coordinateindependent. Its Minkowski analogue gives a version of twistor theory with bothtypes of chiral spinors treated on equal footing. The extensions to the higherrank case with several Heisenberg groups and to the complex case areconsidered. A relation with Riemann theta functions, that are $\QQ$-closed, isdiscussed.

$Sp(8)$ invariant higher spin theory, twistors and geometric BRST formulation of unfolded field equations