This work introduces SpinGlassPEPS$.$jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction algorithms on quasi-2D geometries. In particular, the package employs the Projected Entangled-Pairs States to approximate the Boltzmann distribution corresponding to the model's cost function. This enables an efficient branch-and-bound search (within the probability space) that exploits the locality of the underlying problem's topology. As a result, our software enables the discovery of low-energy configurations for problems on quasi-2D graphs, particularly those relevant to modern quantum annealing devices. The modular architecture of SpinGlassPEPS$.$jl supports various contraction schemes and hardware acceleration.