The anomalous Nernst effect (ANE) - the generation of a transverse electric voltage by a longitudinal heat current in conducting ferromagnets or antiferromagnets - is an appealing approach for thermoelectric power generation in spin caloritronics. The ANE in antiferromagnets is particularly convenient for the fabrication of highly efficient and densely integrated thermopiles as lateral configurations of thermoelectric modules increase the coverage of heat source without suffering from the stray fields that are intrinsic to ferromagnets... In this work, using first-principles calculations together with a group theory analysis, we systematically investigate the spin order-dependent ANE in noncollinear antiferromagnetic Mn-based antiperovskite nitrides Mn$_{3}X$N ($X$ = Ga, Zn, Ag, and Ni). The ANE in Mn$_{3}X$N is forbidden by symmetry in the R1 phase but amounts to its maximum value in the R3 phase. Among all Mn$_{3}X$N compounds, Mn$_{3}$NiN presents the most significant anomalous Nernst conductivity of 1.80 AK$^{-1}$m$^{-1}$ at 200 K, which can be further enhanced if strain, electric, or magnetic fields are applied. The ANE in Mn$_{3}$NiN, being one order of magnitude larger than that in the famous Mn$_{3}$Sn, is the largest one discovered in antiferromagnets so far. The giant ANE in Mn$_{3}$NiN originates from the sharp slope of the anomalous Hall conductivity at the Fermi energy, which can be understood well from the Mott relation. Our findings provide a novel host material for realizing antiferromagnetic spin caloritronics which promises exciting applications in energy conversion and information processing. (read more)