In this paper, we propose two novel second-order distributed algorithms for consensus optimization both employing ADMM as a consensus protocol. The idea is to benefit from the robustness properties of ADMM, on the one hand, and the enhanced performance of Newton-based algorithms, on the other. The designed algorithms use GIANT (a recent second-order optimization method) and Jacobi-like descent directions. We employ tools from system theory, especially singular perturbations, to prove the linear convergence of our distributed schemes with strongly convex costs. We conclude with numerical simulations that confirm our theoretical results and compare the proposed algorithm with state-of-the-art alternatives.