In this paper we demonstrate the first example of a finite translation plane
which does not contain a translation hyperoval, disproving a conjecture of
Cherowitzo. The counterexample is a semifield plane, specifically a Generalised
Twisted Field plane, of order 64. We also relate this non-existence to the
covering radius of two associated rank-metric codes, and the non-existence of
scattered subspaces of maximum dimension with respect to the associated spread