  Answering a question posed by Enriques, we construct a minimal smooth
algebraic surface $S$ of general type over the complex numbers with $K^2 = 45$
and $p_g = 4$, and with birational canonical map. Our surface is a regular
(q=0) ball quotient which is an etale quotient of a Hirzebruch covering of the
plane. The canonical system $|K_S|$ has a fixed part and the degree of the
canonical image is 19.
