At about 2135 Alaska time, the wheel-equipped airplane was substantially damaged when it veered off the runway and collided with a ditch during the landing roll at the Homer Airport. The airplane was operated by the Student pilot/owner, who was accompanied by a flight instructor, neither of whom was injured. Visual conditions prevailed. The flight instructor later reported the student was practicing touch-and-go landings on Runway 21 at Homer; the wind was from 230 degrees at 11 knots. As the airplane touched down, it veered slightly and the student corrected for the swerve. A gust of wind from the right then lifted the right wing, and the airplane began to veer to the left. The student applied right aileron, but the airplane departed off the left side of the paved runway onto an area of grass. The instructor applied engine power in an attempt to gain control of the airplane, but the airplane collided with a ditch that paralleled the runway.