We report a homogeneous quantum cascade laser (QCL) emitting at terahertz (THz) frequencies, with a total spectral emission of about 0.6 THz, centered around 3.3 THz, a current density dynamic range Jdr = 1.53, and a continuous wave output power of 7 mW. The analysis of the intermode beatnote unveils that the devised laser operates as an optical frequency comb (FC) synthesizer over the whole laser operational regime, with up to 36 optically active laser modes delivering ∼200 µW of optical power per optical mode, a power level unreached so far in any THz QCL FC. A stable and narrow single beatnote, reaching a minimum linewidth of about 500 Hz, is observed over a current density range of 240 A/cm2 and even across the negative differential resistance region. We further prove that the QCL FC can be injection locked with moderate radio frequency power at the intermode beatnote frequency, covering a locking range of 1.2 MHz. The demonstration of stable FC operation, in a QCL, over the full current density dynamic range, and without any external dispersion compensation mechanism, makes our proposed homogenous THz QCL an ideal tool for metrological applications requiring mode-hop electrical tunability and a tight control of the frequency and phase jitter.