The propagation and interaction of a randomized 600-ps laser with a helium gas jet were studied experimentally for laser intensities of 10^14 W/cm^2. Such a study is of interest for the indirectly driven inertial confinement fusion scheme, where a randomized laser beam propagates into a gas-filled cavity over a distance of a few millimeters. The dynamics of ionization was studied using time resolved interferometry. Maps of electronic density ne(z,t) were retrieved from time resolved interferograms. The plasma temperature was studied using Thomson scattering. The results show that the laser diffracts while propagating, leading to a decrease in laser intensity and causing ionization to occur later in time. An ionization front, moving at a velocity of about vf≃2.8×10^6 m/s, was observed. Beam diffraction also causes a nonhomogeneous heating of the plasma: the entrance of the plasma is hotter than the exit. A one-dimensional model was used to fit the results. It takes into account collisional ionization and heating by inverse bremsstrahlung. The model shows very good agreement with the experiment.