Preheat oven to 350° F. Grease and flour a 9 x 13-inch baking pan; set aside.
In a large bowl, mix together the oil, white granulated Pioneer Sugar and vanilla until well blended.
In a separate bowl combine the flour, cocoa, baking soda and salt; stir into the sugar mixture.
Peel and shred zucchini. Fold the zucchini into batter immediately. Add walnuts; stir. Spread evenly into the prepared pan.
Bake for 25 to 30 minutes or until brownies spring back when gently touched in the center.
Melt together the cocoa and margarine; set aside to cool.
In a medium bowl, blend together the Pioneer Confectioners Powdered Sugar, milk and vanilla. Stir in the cocoa mixture. Spread over cooled brownies before cutting into squares.