The discovery of materials with improved functionality can be accelerated by rational material design. Heusler compounds with tunable magnetic sublattices allow to implement this concept to achieve novel magnetic properties. Here, we have designed a family of Heusler alloys with a compensated ferrimagnetic state. In the vicinity of the compensation composition in Mn-Pt-Ga, a giant exchange bias (EB) of more than 3 T and a similarly large coercivity are established. The large exchange anisotropy originates from the exchange interaction between the compensated host and ferrimagnetic clusters that arise from intrinsic anti-site disorder. We demonstrate the applicability of our design concept on a second material, Mn-Fe-Ga, with a magnetic transition above room temperature, exemplifying the universality of the concept and the feasibility of room-temperature applications. Our study points to a new direction for novel magneto-electronic devices. At the same time it suggests a new route for realizing rare-earth free exchange-biased hard magnets, where the second quadrant magnetization can be stabilized by the exchange bias.