Ferromagnetic shape-memory CoNiGa alloys have attracted much scientific interest due to their potential alternative use as high-temperature shape-memory alloys, bearing a high prospect for actuation and damping applications at elevated temperatures. Yet, polycrystalline CoNiGa, due to strong orientation dependence of transformation strains, suffers from intergranular fracture. Here, two multi-grain CoNiGa samples were prepared by a novel hot extrusion process that can promote favourable grain-boundary orientation distribution and improve the material's mechanical behaviour. The samples were investigated by multiple methods and their microstructural, magnetic, and mechanical properties are reported. It is found that a post-extrusion solutionising heat treatment leads to the formation of a two-phase oligocrystalline homogeneous microstructure consisting of an austenitic parent B2 phase and γ-CoNiGa precipitates. Reconstruction of the full 3D grain morphology revealed large, nearly spherical grains with no low-angle grain boundaries throughout the entire sample volume. The presence of γ precipitation affects the transformation behaviour of the samples, by lowering the martensitic transformation temperature, while, in conjunction with the oligocrystalline microstructure, it improves the ductility. Controlling the composition of the B2 matrix, as well as the phase fraction of the γ phase, is thus crucial for the optimal behaviour of the alloys.