  We report the detection of outflowing molecular gas at the center of the
nearby radio galaxy NGC6328 (z=0.014), which has a gigahertz-peaked spectrum
radio core and a compact (2 pc) young double radio lobe tracing jet. Utilizing
Atacama Large Millimeter/submillimeter Array (ALMA) CO(2-1) and CO(3-2)
observations, as well as a novel code developed to fit the 3D gas distribution
and kinematics, to study the molecular gas kinematics, we find that the bulk of
the gas is situated within a highly warped disk structure, most likely the
result of a past merger event. Our analysis further uncovers, within the inner
regions of the gas distribution (R<300 pc) and at a position angle aligning
with that of the radio jet (150 degrees), the existence of two anti-diametric
molecular gas structures kinematically detached from the main disk. These
structures most likely trace a jet-induced cold gas outflow with a total lower
limit mass of $2\times 10^6\,\mathrm{M_\odot}$ mass, corresponding to an
outflow rate of $2\,\mathrm{M_\odot\,yr^{-1}}$ and a kinetic power of
$2.7\times 10^{40}\,\mathrm{erg\,s^{-1}}$. The energy required to maintain such
a molecular outflow is aligned with the mechanical power of the jet.
