Context. The text has been edited to adhere to American English based on the spelling style used in the text. In order to anticipate the geoeffectiveness of coronal mass ejections (CMEs), heliospheric simulations are used to propagate transient structures injected at 0.1 AU. Without direct measurements near the Sun, the properties of these injected CMEs must be derived from models coming from observations or numerical simulations, and thus they contain a lot of uncertainty. Aims. 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. Methods. We present the implementation and propagation of modified Titov-Démoulin flux ropes in the COCONUT 3D magnetohydrodynamics coronal model. Background solar wind was reconstructed in order to model two opposite configurations representing a solar activity maximum and minimum, respectively. Both configurations were derived from magnetograms that were obtained by the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory satellite. We tracked the propagation of 24 flux ropes that differ only by their initial magnetic flux. In particular, we investigated the geometry of the flux ropes during the early stages of their propagation as well as the influence of their initial parameters and solar wind configuration on 1D profiles derived at 0.1 AU. Results. At the beginning of the propagation, the shape of the flux ropes varied between simulations during low and high solar activity. We found dynamics that are consistent with the standard CME model, such as pinching of the CME 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 also 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 uncovered relationships between the properties of the magnetic ejecta, such as relationships between density or speed and the initial magnetic flux of our flux ropes. Conclusions. The implementation of the modified Titov-Démoulin flux rope in COCONUT enables us to retrieve the major properties of CMEs at 0.1 AU for any phase of the solar cycle. When combined with heliospheric simulations, COCONUT could lead to more realistic and self-consistent CME evolution models and thus more reliable predictions.