Random lasers are a special class of laser in which light is confined through multiple scattering and interference process in a disordered medium, without a traditional optical cavity. They have been widely studied to investigate fundamental phenomena such as Anderson localization, and for applications such as speckle-free imaging, benefitting from multiple lasing modes. However, achieving controlled localized multi-mode random lasing at long wavelengths, such as in the terahertz (THz) frequency regime, remains a challenge.Here, we study devices consisting of randomly-distributed pillars fabricated from a quantum cascade gain medium, and show that such structures can achieve transversemagnetic polarized (TM) multi-mode random lasing, with strongly localized modes at THz frequencies. The weak short-range order induced by the pillar distribution is sufficient to ensure high quality-factor modes that have a large overlap with the active material.Furthermore, the emission spectrum can be easily tuned by tailoring the scatterer size and filling fraction. These "designer" random lasers, realized using standard photolithography 2 techniques, provide a promising platform for investigating disordered photonics with predesigned randomness in the THz frequency range, and may have potential applications such as speckle-free imaging.