Puzzle #181: Paths

You see a giant chessboard at a park. If you start from the square of your choice and walk from the center of the square to the center of an adjacent (but not diagonally adjacent) square and keep doing this, how long is the shortest route where you have visited each of the 64 squares at least once?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, November 23, 2016 at noon Pacific Time. I will post the answer shortly after.