Mobile impurities interacting with a quantum medium form quasiparticles known as polarons, a central concept in many-body physics. While the quantum impurity problem has been extensively studied with ultracold atomic gases, repulsive polarons in the strongly correlated regime have remained elusive. Typically, the impurity atoms bind into molecules or rapidly decay into deeper-lying states before they can acquire an appreciable dressing cloud. Here, we report on the realization of polarons in a strongly repulsive two-dimensional quantum gas. Using a superfluid of ${}^6$Li dimers, we introduce impurities by promoting a small fraction of the dimers into higher levels of the transverse confining potential. These novel synthetic-spin polarons give access to the strongly repulsive regime where common decay channels are suppressed. We extract key polaron properties—the energy, quasiparticle residue, and effective mass—using trap modulation and Bragg spectroscopy. Our measurements are well captured by a microscopic T -matrix approach and quantum Monte Carlo simulations, revealing deviations from mean-field predictions. In particular, we measure a significant enhancement of the polaron mass, with values exceeding twice the free-dimer mass. Our demonstration of a stable repulsive Bose polaron establishes a platform for studying impurity physics in low-dimensional and strongly correlated systems.