This paper presents a new millimeter-wave sensing system used for near-field imaging applications. The presented system is composed of a parabolic reflector which is fed by an array of compressive antennas. A Compressive Horn Antenna (CHA) is manufactured by inserting a dielectric piece with a pseudo-random geometric pattern inside a Pyramidal Horn Antenna (PHA). The presented CHA is capable of performing spectral coding, which is of special interest for high-sensing-capacity applications. The antenna is fabricated using additive manufacturing (3D printing) techniques and then spray coated with silver. Near-field measurements are carried out in the near-field region of the antenna. The measured fields are then compared with those of the full-wave simulations to validate the performance of the fabricated antenna. Using the surface equivalence principle, the electric and magnetic fields at the aperture of the horn antennas are used to calculate the equivalent radiating electric and magnetic currents. These currents are then integrated to an in-house physical optics-based solver to feed a parabolic reflector and image metallic scatterers in the near-field region of the system. Numerical simulations show that the imaging performance of the reflector fed by the CHAs outperforms those of the reflector fed by PHAs.