We aim to give a full description of the distribution and location of dense molecular clouds in the giant molecular cloud complex W43. It has previously been identified as one of the most massive star-forming regions in our Galaxy. To trace the moderately dense molecular clouds in the W43 region, we initiated an IRAM 30m large program, named W43-HERO, covering a large dynamic range of scales (from 0.3 to 140 pc). We obtained on-the-fly-maps in 13CO (2-1) and C18O (2-1) with a high spectral resolution of 0.1 km/s and a spatial resolution of 12". These maps cover an area of ~1.5 square degrees and include the two main clouds of W43, as well as the lower density gas surrounding them. A comparison with Galactic models and previous distance calculations confirms the location of W43 near the tangential point of the Scutum arm at a distance from the Sun of approximately 6 kpc. The resulting intensity cubes of the observed region are separated into sub-cubes, centered on single clouds which are then analyzed in detail. The optical depth, excitation temperature, and H2 column density maps are derived out of the 13CO and C18O data. These results are then compared with those derived from Herschel dust maps. The mass of a typical cloud is several 10^4 solar masses while the total mass in the dense molecular gas (>100 cm^-3) in W43 is found to be about 1.9e6 solar masses. Probability distribution functions obtained from column density maps derived from molecular line data and Herschel imaging show a log-normal distribution for low column densities and a power-law tail for high densities. A flatter slope for the molecular line data PDF may imply that those selectively show the gravitationally collapsing gas.