  We incorporate a massless scalar field into a 3-dimensional code for the
characteristic evolution of the gravitational field. The extended 3-dimensional
code for the Einstein--Klein--Gordon system is calibrated to be second order
convergent. It provides an accurate calculation of the gravitational and scalar
radiation at infinity. As an application, we simulate the fully nonlinear
evolution of an asymmetric scalar pulse of ingoing radiation propagating toward
an interior Schwarzschild black hole and compute the backscattered scalar and
gravitational outgoing radiation patterns. The amplitudes of the scalar and
gravitational outgoing radiation modes exhibit the predicted power law scaling
with respect to the amplitude of the initial data. For the scattering of an
axisymmetric scalar field, the final ring down matches the complex frequency
calculated perturbatively for the $\ell=2$ quasinormal mode.
