  We introduce in this article a new method to estimate the minimum distance of
codes from algebraic surfaces. This lower bound is generic, i.e. can be applied
to any surface, and turns out to be ``liftable'' under finite morphisms, paving
the way toward the construction of good codes from towers of surfaces. In the
same direction, we establish a criterion for a surface with a fixed finite set
of closed points $\mathcal P$ to have an infinite tower of $\ell$--\'etale
covers in which $\mathcal P$ splits totally. We conclude by stating several
open problems. In particular, we relate the existence of asymptotically good
codes from general type surfaces with a very ample canonical class to the
behaviour of their number of rational points with respect to their $K^2$ and
coherent Euler characteristic.
