Bake the cake according to the back of the box. Right before the cake comes out of the oven, combine the pudding mix, milk, Andes baking chips, & peppermint extract. Whisk for one minute. Take the cake out of the oven, and poke holes all over it with the back of a wooden spoon. Pour on the pudding mixture. Spread it all over using a spatula, taking care be sure the pudding is getting inside of the holes. Refrigerate until completely chilled, about 1 hour.