High-Harmonic Generation (HHG) spectra of randomly aligned bromoform (CHBr3) molecules have been experimentally measured and theoretically simulated at various laser pulse intensities. From the experiments, we obtained a significant number of harmonics that goes beyond the cutoff limit predicted by the three-step model (3SM) with ionization from HOMO. To interpret the experiment, we resorted to real-time time-dependent configuration interaction with single excitations. We found that electronic bound states provide an appreciable contribution to the harmonics. More in detail, we analyzed the electron dynamics by decomposing the HHG signal in terms of single molecular-orbital contributions, to explain the appearance of harmonics around 20-30 eV beyond the expected cutoff due to HOMO. HHG spectra can be therefore explained by considering the contribution at high energy of HOMO-6 and HOMO-9, thus indicating a complex multiple-orbital strong-field dynamics. However, even though the presence of the bromoform cation should be not enough to produce such a signal, we could not exclude a priori that the origin of harmonics in the H29-H45 to be due to the cation, which has more energetic ionization channels.