We probed, in the time domain, the THz electromagnetic radiation originating from spins in CdMnTe diluted magnetic semiconductor quantum wells containing high-mobility electron gas. Taking advantage of the efficient Raman generation process, the spin precession was induced by low power near-infrared pulses. We provide a full theoretical first-principles description of spin-wave generation, spin precession, and of emission of THz radiation. Our results open new perspectives for improved control of the direct coupling between spin and an electromagnetic field, e.g., by using semiconductor technology to insert the THz sources in cavities or pillars.