Carbon-based synthetic lattices offer a versatile platform for the realization and control of correlated quantum effects at the nanoscale. Advances in on-surface synthesis have facilitated the fabrication of increasingly complex molecular frameworks, opening new avenues for the exploration and engineering of custom tailored electronic and magnetic phases. Here, we report the design, on-surface synthesis, and characterization of a two-dimensional (2D) covalent organic framework (COF) assembled from D3h symmetric S = 3/2 [4]triangulene building blocks arranged in a honeycomb structure. Combined scanning probe microscopy and spectroscopy, corroborated by first-principles density functional theory (DFT) and GW calculations, establish an antiferromagnetic (AFM) insulating ground state. Low energy spectroscopy resolves spin excitations in both one-dimensional (1D) chains and extended 2D networks, providing direct insight into the emergent spin dynamics and establishing a modular platform to explore quantum magnetism in a pi-conjugated organic system.