  We analyze the class of four-dimensional N = 4 supergravities obtained by
gauging the axionic shift and axionic rescaling symmetries. These theories are
formulated with the machinery of embedding tensors and shown to be deducible
from higher dimensions using a Scherk--Schwarz reduction with a twist by a
non-compact symmetry. This allows to evade the usual unimodularity requirement
and completes the dictionary between heterotic gaugings and fluxes, at least
for the "geometric sector".
