Exchange bias corresponds to a shift of the hysteresis loop of a ferromagnet along the magnetic field axis due to interfacial exchange coupling with an adjacent antiferromagnetic layer. It is used for a variety of technological applications, including magnetoresistive read heads and sensors. Though both FM and AFM subsystems are inseparable parts of an exchange bias system, it is the latter that determines the magnitude of the exchange bias in the system. Therefore, it is important to search for an appropriate magnetically compensated material to observe a maximum effect. In this regard, we have designed compensated ferrimagnetic systems Mn3-xPtxGa and Mn2-xFe1+xGa. By optimizing the Mn/Pt ratio in the bulk Mn3-xPtxGa, we observe a giant exchange bias of more than 3 T and a similarly large coercivity in the vicinity of the compensated point. For application prospective we focus to prepare thin films of these samples. We are also looking forward to use these materials as a pinning layer in FM/AFM heterogeneous exchange bias systems .