Methanol masers at 6.7 GHz are well known tracers of high-mass star-forming regions. However, their origin is still not clearly understood. We aimed to determine the morphology and velocity structure for a large sample of the maser emission with generally lower peak flux densities than those in previous surveys. Using the European VLBI Network we imaged the remaining sources (17) from a sample of sources that were selected from the unbiased survey using the Torun 32 m dish. Together they form a database of a total of 63 source images with high sensitivity, milliarcsecond angular resolution and very good spectral resolution for detailed studies. We studied in detail the properties of the maser clouds and calculated the mean and median values of the projected size (17.4 au and 5.5 au, respectively) as well as the FWHM of the line (0.373 km s$^{-1}$ and 0.315 km s$^{-1}$ for the mean and median values, respectively), testing whether it was consistent with Gaussian profile. We also found maser clouds with velocity gradients (71 per cent) that ranged from 0.005 km s$^{-1}$ au$^{-1}$ to 0.210 km s$^{-1}$ au$^{-1}$. We tested the kinematic models to explain the observed structures of the 6.7 GHz emission. There were targets where the morphology supported the scenario of a rotating and expanding disk or a bipolar outflow. Comparing the interferometric and single-dish spectra we found that, typically, 50-70 per cent of the flux was missing. This phenomena is not strongly related to the distance of the source. The EVN imaging reveals that in the complete sample of 63 sources the ring-like morphology appeared in 17 per cent of sources, arcs were seen in a further 8 per cent, and the structures were complex in 46 per cent cases. The UC HII regions coincide in position in the sky for 13 per cent of the sources. They are related both to extremely high and low luminosity masers from the sample.
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