Finding the optimal coalition structure is an NP-complete problem that is computationally challenging even under quite restrictive assumptions. In this paper, we propose a new algorithm for the Coalition Structure Generation (CSG) problem, which provides good enough quality solutions and that can be run with hundreds of agents. The Fast code-based Algorithm for Coalition Structure generation (FACS) uses a novel representation of the search space of coalition structures and a new code-based search technique. We devise an effective heuristic search method to efficiently explore the space of coalition structures using our code-based technique. Results show that our method outperforms existing state-of-the-art algorithms by multiple orders of magnitude while providing high-quality solutions.