Ferromagnetic Ni2MnGa-based alloys play an important role in technological fields, such as smart actuators, magnetic refrigeration and robotics. The possibility of obtaining large non-contact deformation induced by an external perturbation is one of its key strengths for applications. However, the search for materials with low cost, practical fabrication procedures and large signal output under small perturbing fields still poses challenges. In the present study we demonstrate that by judicial choice of substitution on the Mn site, an abrupt magnetostructural transition from a paramagnetic austenite phase to a ferromagnetic martensite one can be tuned to close to room temperature achieving large and reproducible strains. The required magnetic field to induce the strain varies from small values, as low as 0.25 T for 297.4 K and 1.6% of strain, to 8 T for 305 K and 2.6% of strain. Our findings point to encouraging possibilities for application of shape memory alloys in relatively inexpensive, scalable polycrystalline materials.