Robust wave propagation along the boundaries of two-dimensional structures at frequencies of bulk bandgap is the subject of active study and is typically related to topological properties. Here, we propose a new model of two-dimensional (2D) structure which is composed of centimeter-scale bianisotropic dielectric resonators placed in the nodes of a square lattice and supports edge states at microwave frequencies. As we demonstrate, bianisotropy  introduced by breaking a geometrical symmetry of cylindrical resonators is essential for the bandgap opening. The simulation results for a finite structure demonstrate the emergence of in-gap edge states at the interface between  the domains with oppositely oriented bianisotropic resonators. We numerically demonstrate spin-momentum locking for these modes, and, moreover, the emergence of such edge states at the boundary between the structure and  free space, which is unusual for photonic topological insulators. The resilience of the observed states is confirmed by studying the system with double-bend interface and geometrical imperfections.