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(3 − 2) and CO(2 − 1) 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°), 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 × 106 M⊙ mass, corresponding to an outflow rate of 2 M⊙ yr−1 and a kinetic power of 2.7 × 1040 erg s−1. The energy required to maintain such a molecular outflow is aligned with the mechanical power of the jet.