  An exact S-matrix is conjectured for the imaginary coupled d_4(3) affine Toda
field theory, using the U_q(g_2(1)) symmetry. It is shown that this S-matrix is
consistent with the results for the case of real coupling using the
breather-particle correspondence. For q a root of unity it is argued that the
theory can be restricted to yield Phi(11|14) perturbations of WA_2 minimal
models and the restriction is performed for the (3,p') minimal models.
