Within the framework of two-dimensional discrete elasticity, this study investigates the propagation of elastic waves in a planar solid composed of a metamaterial whose microstructure is engineered according to the Heuristic Molecules approach proposed by Casolo [1]. The RBSM-HM formulation enables the design of discrete topologies consisting of rigid elements (Heuristic Atoms) interconnected by elastic links to form Heuristic Molecules, leading to macroscopically isotropic and centrosymmetric assemblies exhibiting micropolar properties in the linear-elastic static regime. The periodic unit cell comprises two types of elastic interactions between first-order neighbours: blue axial non-central springs and magenta shear springs. In addition, two red springs connecting second-order neighbours account for central interactions along the cell diagonals. By appropriately calibrating these elastic connections, the macroscopic response of the assembly can be tailored to represent different continuum materials, ranging from a classical Cauchy continuum to the isotropic micropolar Cosserat continuum considered in the present study. The investigation is then extended to the dynamic regime to assess the influence of the discrete topology and characteristic length scales of the microstructure on elastic wave propagation. The interaction between the spectral content of the propagating waves and the characteristic properties of the microstructured medium may give rise to dispersion, and other features of the dynamic response. Rectangular beams with different slenderness ratios are adopted as case studies for a parametric numerical investigation performed using a dedicated MATLAB code. The numerical results clearly reveal the relationship between the spectral characteristics of the propagating waves and those associated with the underlying microstructure, highlighting distinctive features of the elastodynamic behaviour of the medium, particularly in terms of wave dispersion and coherence of signal propagation.