  In this article we study the bicanonical map $\phi_2$ of quadruple Galois
canonical covers X of surfaces of minimal degree. We show that $\phi_2$ has
diverse behavior and exhibit most of the complexities that are possible for a
bicanonical map of surfaces of general type, depending on the type of X. There
are cases in which $\phi_2$ is an embedding, and if so happens, $\phi_2$ embeds
$X$ as a projectively normal variety, and cases in which $\phi_2$ is not an
embedding. If the latter, $\phi_2$ is finite of degree 1, 2 or 4. We also study
the canonical ring of X, proving that it is generated in degree less than or
equal to 3 and finding the number of generators in each degree. For generators
of degree 2 we find a nice general formula which holds for canonical covers of
arbitrary degrees. We show that this formula depends only on the geometric and
the arithmetic genus of X.
