You can simply activate further your material by physical activation with steam. As physical activation is a mild gasification, all pores are broadened, so that the surface area first increases (as more pores are created), then decreases (as these pores become wider and wider).
The are a number of activators and templates for obtaining carbon with large pore size. however, I would give preference to MgO as a template for large pore size in the activated carbon. You can simply mix MgO with carbon precursor either in powder form or dispersing it in a solvent with carbon precursor. Followed by drying and carbonizing and then washing to remove MgO.