  We discover a family of surfaces of general type with $K^2=3$ and $p=q=0$ as
free $C_{13}$ quotients of special linear cuts of the octonionic projective
plane $\mathbb O \mathbb P^2$. A special member of the family has $3$
singularities of type $A_2$, and is a quotient of a fake projective plane. We
use the techniques of \cite{BF20} to define this fake projective plane by
explicit equations in its bicanonical embedding.
