In a large bowl, cream together the sugars, butter or margarine and oil. Add eggs, vanilla and buttermilk; stir well to mix. Sift together all dry ingredients and then sift into the mixing bowl. Grate the zucchini, skin and all, into the bowl and stir until blended. Pour into a greased and floured 9 x 13-inch baking pan. Sprinkle top with chocolate pieces and bake in a preheated 350° oven for 45 minutes, or until cake tests done. Additional frosting is optional but not necessary.