  The generalized Kerr-Schild ansatz (GKSA) is a powerful tool for constructing
exact solutions in Double Field Theory (DFT). In this paper we focus in the
heterotic formulation of DFT, considering up to four-derivative terms in the
action principle, while the field content is perturbed by the GKSA. We study
the inclusion of the generalized version of the Green-Schwarz mechanism to this
setup, in order to reproduce the low energy effective heterotic supergravity
upon parametrization. This formalism reproduces higher-derivative heterotic
background solutions where the metric tensor and Kalb-Ramond field are
perturbed by a pair of null vectors. Next we study higher-derivative
contributions to the classical double copy structure. After a suitable
identification of the null vectors with a pair of $U(1)$ gauge fields, the
dynamics is given by a pair of Maxwell equations plus higher derivative
corrections in agreement with the KLT relation.
