We analyzed the observations of scintillations in a laser beam (532 nm, ~200 mW power) traveling along a 144 km path at an altitude of 2.2-2.4 km above sea level, just above the atmospheric boundary layer, between the islands of La Palma and Tenerife. The observations were performed during nighttime on 18 July 2011, by means of a telescope with an aperture diameter of 1 m. Strong scintillations were observed. The estimates of spatial spectra and correlation functions indicated that the observed intensity fields possess, statistically, a locally isotropic structure, which agrees with the idea of a locally isotropic turbulence. The estimates of spatial autospectra and autocorrelation functions of the intensity field indicated that the characteristic scale of the internal structure of the observed clusters is 6.5-8 mm, while the characteristic size of the clusters is 4-5 cm. The major contribution to the observed scintillations comes from the inhomogeneities of the intensity field with scales from 1-2 cm up to 10-12 cm. The analysis of the cross-spectra indicated that the hypothesis of frozen turbulence introduced by Taylor can be used for the description of spatiotemporal structure of intensity fluctuations of laser beams traveling through long paths in the atmosphere.