Based on a new implementation of the TDKS or or "real-time TDDFT" method in the Q-Chem code, we have tested the TDKS approach for simulation of high harmonic spectra using atom-centered Gaussian basis functions and an atom-centered, real-space CAP. In these strong-field simulations, the CAP serves to absorb the highest-energy part of the outgoing charge density wave, representing tunneling ionization, which would otherwise reflect off of the artificial barrier that is created by the finite extent of the basis set. Interference between the outgoing and reflected waves then leads to significant noise in the high harmonic spectrum obtained from the fluctuating dipole moment function.