In recent years, antiferromagnetic spintronics has received much attention since ideal antiferromagnets do not produce stray fields and are much more stable to external magnetic fields compared to materials with net magnetization. Akin to antiferromagnets, compensated ferrimagnets have zero net magnetization but have the potential for large spin-polarization and strong out of plane magnetic anisotropy, and, hence, are ideal candidates for high density memory applications. Here, we demonstrate that a fully compensated magnetic state with a tunable magnetic anisotropy is realized in Mn-Pt-Ga based tetragonal Heusler thin films. Furthermore, we show that a bilayer formed from a fully compensated and a partially compensated Mn-Pt-Ga layer, exhibits a large interfacial exchange bias up to room temperature. The present work establishes a novel design principle for spintronic devices that are formed from materials with similar elemental compositions and nearly identical crystal and electronic structures. Such devices are of significant practical value due to their improved properties such as thermal stability. The flexible nature of Heusler materials to achieve tunable magnetizations, and anisotropies within closely matched materials provides a new direction to the growing field of antiferromagnetic spintronics.