  Two-dimensional (spin-$2$) Affleck-Kennedy-Lieb-Tasaki (AKLT) type valence
bond solids on the square lattice are known to be symmetry protected
topological (SPT) gapped spin liquids [Shintaro Takayoshi, Pierre Pujol, and
Akihiro Tanaka Phys. Rev. B ${\bf 94}$, 235159 (2016)]. Using the projected
entangled pair state (PEPS) framework, we extend the construction of the AKLT
state to the case of $SU(3)$, relevant for cold atom systems. The entanglement
spectrum is shown to be described by an alternating $SU(3)$ chain of "quarks"
and "antiquarks", subject to exponentially decaying (with distance) Heisenberg
interactions, in close similarity with its $SU(2)$ analog. We discuss the SPT
feature of the state.
