High energy γ rays from Giant Molecular Clouds (GMCs) carry direct information about the spatial and energy distributions of Galactic Cosmic Rays (CRs). The recently released catalogs of GMCs contain sufficiently massive clouds to be used as barometers for probing, through their γ-ray emission, the density of CRs throughout the Galactic Disk. Based on the data of Fermi-LAT , we report the discovery of γ-ray signals from nineteen GMCs located at distances up to 12.5 kpc. The galactocentric radial distribution of the CR density derived from the γ-ray and CO observations of these objects, as well as from some nearby clouds that belong to the Gould Belt complex, unveil a homogeneous "sea" of CRs with a constant density and spectral shape close to the flux of directly (locally) measured CRs. We found noticeable deviations from the "sea level" only in some locations characterized by enhanced CR density in the galactocentric 4-6 kpc ring. Furthermore, we found a hint for fluctuations of the CR density in different locations within the same 4-6 kpc ring. The confirmation of this result with the next-generation γ-ray detectors based on the higher quality data and denser coverage of galactocentric distances, would have dramatic implications for the understanding of the origin of Galactic CRs.PACS numbers: 95.85.Ry; 98.70.Sa