Context. Water-fountain nebulae are asymptotic giant branch (AGB) and post-AGB objects that exhibit high-velocity outflows traced by water-maser emission. Their study is important for understanding the interaction between collimated jets and the circumstellar material that leads to the formation of bipolar and/or multi-polar morphologies in evolved stars. Aims. The aim of this paper is to describe the three-dimensional morphology and kinematics of the molecular gas of the water-fountain nebula IRAS 16342−3814. Methods. Data was retrieved from the ALMA archive for analysis using a simple spatio-kinematical model. The software SHAPE was employed to construct a three-dimensional, spatio-kinematical model of the molecular gas in IRAS 16342−3814, and to then reproduce the intensity distribution and position-velocity diagram of the CO emission from the ALMA observations to derive the morphology and velocity field of the gas. Data from CO(J = 1 → 0) supported the physical interpretation of the model. Results. A spatio-kinematical model that includes a high-velocity collimated outflow embedded within material expanding at relatively lower velocity reproduces the images and position-velocity diagrams from the observations. The derived morphology is in good agreement with previous results from IR and water-maser emission observations. The high-velocity collimated outflow exhibits deceleration across its length, while the velocity of the surrounding component increases with distance. The morphology of the emitting region, the velocity field, and the mass of the gas as function of velocity are in excellent agreement with the properties predicted for a molecular outflow driven by a jet. The timescale of the molecular outflow is estimated to be ~70–100 yr. The scalar momentum carried by the outflow is much larger than it can be provided by the radiation of the central star. An oscillating pattern was found associated with the high-velocity collimated outflow. The oscillation period of the pattern is T ≈ 60–90 yr and its opening angle is θop ≈ 2°. Conclusions. The CO (J = 3 → 2) emission in IRAS 16342−3814 is interpreted in terms of a jet-driven molecular outflow expanding along an elongated region. The position-velocity diagram and the mass spectrum reveal a feature due to entrained material that is associated with the driving jet. This feature is not seen in other more evolved objects that exhibit more developed bipolar morphologies. It is likely that the jet in those objects has already disappeared since it is expected to last only for a couple hundred years. This strengthens the idea that water fountain nebulae are undergoing a very short transition during which they develop the collimated outflows that shape the circumstellar envelopes. The oscillating pattern seen in the CO high-velocity outflow is interpreted as due to precession with a relatively small opening angle. The precession period is compatible with the period of the corkscrew pattern seen at IR wavelengths. We propose that the high-velocity molecular outflow traces the underlying primary jet that produces such a pattern.
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