  We study the behavior of the bilinkage process in codimension $3$. In
particular, we construct a smooth canonically embedded and linearly normal
surface of general type of degree $18$ in $\mathbb{P}^5$, this is probably the
highest degree such surface may have. Next, we apply our construction to find a
geometric description of Tonoli Calabi--Yau threefolds in $\mathbb{P}^6$.
