Inelastic-neutron-scattering measurements were performed on a single crystal of the heavy-fermion paramagnet UTe2 above its superconducting temperature. We confirm the presence of antiferromagnetic fluctuations with the incommensurate wave-vector k1=(0,0.57,0). A quasielastic signal is found, whose momentum-transfer dependence is compatible with fluctuations of magnetic moments a with a sine-wave modulation of wave-vector k1 and in-phase moments on the nearest U atoms. Low dimensionality of the magnetic fluctuations, consequence of the ladder structure, is indicated by weak correlations along the direction c. These fluctuations saturate below the temperature T1∗≃15K, in possible relation with anomalies observed in thermodynamic, electrical-transport, and nuclear-magnetic-resonance measurements. The absence or weakness of ferromagnetic fluctuations in our data collected at temperatures down to 2.1 K and energy transfers from 0.6 to 7.5 meV is emphasized. These results constitute constraints for models of magnetically mediated superconductivity in UTe2.