We present THz range optical conductivity data of a thin film of the near quantum critical heavy fermion compound CeFe$_2$Ge$_2$. Our complex conductivity measurements find a deviation from conventional Drude-like transport in a temperature range previously reported to exhibit unconventional behavior. We calculate the frequency dependent effective mass and scattering rate using an extended Drude model analysis. We find the inelastic scattering rate can be described by a temperature dependent power-law $omega^{n(T)}$ where $n(T)$ approaches $sim1.0 pm 0.2$ at 1.5 K. This is compared to the $rho sim T^{1.5}$ behavior claimed in dc resistivity data and the $rho sim T^{2}$ expected from Fermi-liquid theory. In addition to a low temperature mass renormalization, we find an anomalous mass renormalization that persists to high temperature. We attribute this to a Hunds coupling in the Fe states in a manner similar to that recently proposed in the ferro-pnictides. CeFe$_2$Ge$_2$ appears to be a very interesting system where one may study the interplay between the usual $4f$ lattice Kondo effect and this Hunds enhanced Kondo effect in the $3d$ states.
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