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The aim of this paper is to demonstrate the possible use of the new coronal model COCONUT to compute a detailed representation of a numerical CME at 0.1~AU, after its injection at the solar surface and propagation in a realistic solar wind, as derived from observed magnetograms. We present the implementation and propagation of modified Titov-D\'emoulin (TDm) flux ropes in the COCONUT 3D MHD coronal model. The background solar wind is reconstructed in order to model two opposite configurations representing a solar activity maximum and minimum respectively. Both were derived from magnetograms which were obtained by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamic Observatory (SDO) satellite. We track the propagation of 24 flux ropes, which differ only by their initial magnetic flux. We especially investigate the geometry of the flux rope during the early stages of the propagation as well as the influence of its initial parameters and solar wind configuration on 1D profiles derived at 0.1~AU. At the beginning of the propagation, the shape of the flux ropes varies between simulations during low and high solar activity. We find dynamics that are consistent with the standard CME model, such as the pinching of the legs and the appearance of post-flare loops. Despite the differences in geometry, the synthetic density and magnetic field time profiles at 0.1~AU are very similar in both solar wind configurations. These profiles are similar to those observed further in the heliosphere and suggest the presence of a magnetic ejecta composed of the initially implemented flux rope and a sheath ahead of it. Finally, we uncover relationships between the properties of the magnetic ejecta, such as density or speed and the initial magnetic flux of our flux ropes., Comment: 20 pages, 13 figures