We investigate the features of multimode steady-state generation of the superradiant heterolasers which have an active medium formed by the quantum dots with long incoherent relaxation time and a cavity of a combined Fabry-Perot type with a distributed feedback of the counter-propagating waves. We show that a quantum-coherent dynamics of the optical dipole oscillations and a population inversion of the working levels in an ensemble of the quantum dots with a strong inhomogeneous broadening of a spectral line may lead to a simultaneous lasing of modes with a various degree of phasing and/or correlation and with qualitatively different dynamical behavior, including quasi-stationary, metastable, self-modulated, pulsed-periodic, quasi-chaotic ones.