  As a step towards quantization of Higher Spin Gravities we construct the
presymplectic AKSZ sigma-model for $4d$ Higher Spin Gravity which is AdS/CFT
dual of Chern-Simons vector models. It is shown that the presymplectic
structure leads to the correct quantum commutator of higher spin fields and to
the correct algebra of the global higher spin symmetry currents. The
presymplectic AKSZ model is proved to be unique, it depends on two coupling
constants in accordance with the AdS/CFT duality, and it passes some simple
checks of interactions.
