  The dimensions of the spaces of $k$-homogeneous $\mathrm{Spin}(9)$-invariant
valuations on the octonionic plane are computed using results from the theory
of differential forms on contact manifolds as well as octonionic geometry and
representation theory. Moreover, a valuation on Riemannian manifolds of
particular interest is constructed which yields, as a special case, an element
of $\mathrm{Val}_2^{\mathrm{Spin}(9)}$.
