  We begin with the higher-weight modular symbols introduced by Shokurov, which
generalize Manin's weight-2 modular symbols. We then define higher-weight
limiting modular symbols associated to vertical geodesics with one endpoint at
an irrational real number, by means of a limiting procedure on Shokurov's
modular symbols. These are analogous to the Manin-Marcolli limiting modular
symbols for the weight-2 case, which are given by a similar limiting procedure
on the Manin modular symbols. We show that the limit defining the higher-weight
limiting modular symbol is equivalent everywhere to a limit given by
approximating the irrational endpoint by its continued fraction expansion. This
is done by means of shifting to a coding space, as in the approach of
Kesseb\"ohmer and Stratmann in the weight-2 case.
