Cut your pieces from the 3/4-inch thick plywood. Cut two side pieces 4-by-24 inches, one bottom piece 22 1/2-by-10 inches and two ends 10-by-10 inches. Cut one piece of 1 1/2-inch round dowel 22 1/2 inches long. Cut the pieces on a table saw.
Mark a line across the end pieces, 4 inches from one edge with a square. Mark a line perpendicular to the first line in the center of each end piece, and a line 1 1/2 inches on either side of the center line. Draw diagonal lines between the ends of the line you drew 4 inches from one edge to the ends of the outside perpendicular lines, 6 inches above. Cut along these diagonal lines with a jigsaw.
Glue and nail the two end pieces to the ends of the bottom, with the "peak" up. Use 1 1/2-inch nails in a pin nail gun. Align the ends with the 10-inch edges flush with the bottom of the bottom piece. Nail through the end pieces into the edge of the bottom piece. Glue and nail the two side pieces on the outside of the box, with the two narrow ends flush with the outside faces of end pieces and one long edge flush the bottom of the bottom piece.
Mark the outside face of each end piece 3/4 inch from the top on the center vertical line. Bore a 1/8-inch hole through each end. Fit the dowel between the ends of the box and drive a 3-inch treated deck screw through each end piece into the ends of the dowel to secure the handle.