Teaser 2905: Trackword

From The Sunday Times, 27th May 2018 [link]

George and Martha are tackling a Trackword problem which appears in magazines. Nine letters are placed in a 3×3 grid and you have to work from one square to a neighbour, proceeding up, down, left, right or diagonally until all nine squares have been visited to form a nine-letter word. You must start in the top-left corner. As an example, you can get the word EIGHTFOLD from the following grid:

George and Martha thought that would be interesting to work out how many possible routes there are which start in the top-left corner.

How many routes are there?