  Cayley cones in the octonions $\mathbb{O}$ that are ruled by oriented
2-planes are equivalent to pseudoholomorphic curves in the Grassmannian of
oriented 2-planes G(2,8). The well known twistor fibration $G(2,8) -> S^6$ is
used to prove the existence of immersed higher-genus pseudoholomorphic curves
in $\gro$. Equivalently, this produces Cayley cones whose links are
$S^1$-bundles over genus-$g$ Riemann surfaces. When the degree of an immersed
pseudoholomorphic curve is large enough, the corresponding 2-ruled Cayley cone
is the asymptotic cone of a non-conical 2-ruled Cayley 4-fold.
