At the expense of frequency narrowing, binary amplitude-only diffractive optical elements emulate refractive lenses without the need of large profiles. Unfortunately, they also present larger Fresnel reflection loss than conventional lenses. This is usually tackled by implementing unattractive cumbersome designs. Here we demonstrate that simplicity is not at odds with performance and we show how the fishnet metamaterial can improve the radiation pattern of a Soret lens. The building block of this advanced Soret lens is the fishnet metamaterial operating in the near-zero refractive index regime with one of the edge layers designed with alternating opaque and transparent concentric rings made of subwavelength holes. The hybrid Soret fishnet metalens retains all the merits of classical Soret lenses such as low profile, low cost and ease of manufacturing. It is designed for the W-band of the millimeter-waves range with a subwavelength focal length FL = 1.58 mm (0.5λ0) aiming at a compact antenna or radar systems. The focal properties of the lens along with its radiation characteristics in a lens antenna configuration have been studied numerically and confirmed experimentally, showing a gain improvement of ~2 dB with respect to a fishnet Soret lens without the fishnet metamaterial.