  We revisit the construction of the $\mathcal{N}=1$ supersymmetric
trinification models with gauge group $\mathrm{U}(3)_C\times \mathrm{U}(3)_L
\times \mathrm{U}(3)_R$ in Type IIA string theory on
$\mathbf{T^6/(\mathbb{Z}_2\times \mathbb{Z}_2)}$ orientifold with intersecting
D6-branes. The non-trivial K-theory conditions and tadpole cancellation
conditions severely restrict the number of allowed models even for the case of
rectangular two-tori. Using a supervised search algorithm, we find a few
four-family models where the highest wrapping number is 2. For these models, we
present the complete particle spectra and the gauge coupling relations at the
string-scale.
