  We study $\mathbb{C}P^2$ Skyrmion crystals in the ferromagnetic SU(3)
Heisenberg model with a generalization of the Dzyaloshinskii-Moriya interaction
and the Zeeman term. The model possesses two different types of Skyrmion
crystals with unit-Skyrmions that can be interpreted as bound states of two
half-Skyrmions or four quarter-Skyrmions. Our study on $\mathbb{C}P^2$ Skyrmion
crystals opens up the possibility for useful future applications since
$\mathbb{C}P^2$ Skyrmions have more degrees of freedom than the usual
$\mathbb{C}P^1$ (magnetic) Skyrmions.
