Feedback from black-hole-powered jets has been invoked in many cosmological simulations to regulate star formation and quench galaxies. Despite this, observational evidence of how jets might be able to affect their hosts remains scarce, especially for low-power jets in halos smaller than clusters. Recent observations of outflows around FR0 galaxies, which host compact radio-loud sources, imply that lower-power jetted active galactic nuclei (AGN) may have a significant impact on their hosts through jet interactions with the interstellar medium (ISM). Using the Arepo code, we launch jets of low and intermediate power (10(38)-10(43) erg s(-1)) within a similar to kiloparsec-scale periodic box with driven turbulence, to study how the jets propagate through a turbulent ISM. Our simulation results broadly fit into three different scenarios-jets penetrating easily through the ISM, becoming completely stalled, or, an interesting intermediate stage, jets being highly disturbed and redirected. We suggest that intermediate-power jets do not have enough ram pressure to affect the turbulent structure of the ISM and so only fill preexisting cavities. Low-power jets are able to drive outflows in a hot phase (>10(4.4) K). However, warm (similar to 10(4) K) ionized gas outflows appear under certain conditions. This work is part of the "Learning the Universe" collaboration, aiming to build next-generation cosmological simulations that incorporate a new prescription for AGN feedback.