Quasi-crystal distributed feedback lasers do not require any form of mirror cavity to amplify and extract radiation. Once implemented on the top surface of a semiconductor laser, a quasi-crystal pattern can be used to tune both the radiation feedback and the extraction of highly radiative and high-quality-factor optical modes that do not have a defined symmetric or anti-symmetric nature. Therefore, this methodology offers the possibility to achieve efficient emission, combined with tailored spectra and controlled beam divergence. Here, we apply this concept to a one-dimensional quantum cascade wire laser. By lithographically patterning a series of air slits with different widths, following the Octonacci sequence, on the top metal layer of a double-metal quantum cascade laser operating at THz frequencies, we can vary the emission from single-frequency-mode to multimode over a 530-GHz bandwidth, achieving a maximum peak optical power of 240 mW (190 mW) in multimode (single-frequency-mode) lasers, with record slope efficiencies for multimode surface-emitting disordered THz lasers up to ≈570 mW/A at 78 K and ≈720 mW/A at 20 K and wall-plug efficiencies of η ≈ 1%.