Preheat oven to 350 degrees. Line a 9x13" baking pan with parchment paper.
Grate zucchini on small holes of grater and place in bowl while you mix the rest of the cake.
Beat eggs, vegetable oil, applesauce, sugar, and vanilla together in a large bowl with a whisk.
In a separate small bowl whisk together the flour, baking powder, baking soda, cinnamon, salt, and nutmeg.
Add dry ingredients to egg mixture ,mixing with a spatula just until incorporated. Drain the liquid from the zucchini and fold in zucchini (should measure about 2 cups) and raisins stirring until completely mixed in. Pour batter into prepared 9x13" pan and smooth top
Bake for 30-35 minutes or until toothpick inserted into the centre comes out clean.
While the cake cools, beat together frosting ingredients with a hand mixer and spread over the top of the cooled cake.