We show that the nonadiabatic (non-Born-Oppenheimer) ground state of a three-nuclei system can be effectively calculated with the use of an explicitly correlated Gaussian basis set with floating centers. Sample calculations performed for the H2D+ system with various basis set sizes show good convergence with respect to both the total energy and the expectation values of the internuclear distances (molecular geometry), the distances between the nuclei and the electrons, and between the electrons. We also provide a derivation of the formulas for one-particle density calculations and some density plots showing the spatial distribution of the H2D+ nuclear and electronic densities.