Preheat the oven to 350 degrees and grease a standard loaf pan.
Grate the zucchini and set it aside.
In a medium bowl, whisk the flour, baking powder, baking soda, cinnamon, and salt. Set aside.
In a large bowl, stir together the eggs, maple syrup, avocado oil, coconut milk, and vanilla. Stir in the flour mixture, then add the grated zucchini and stir.
Transfer the batter to the greased loaf pan. Spread the top of the batter to even it out. Bake for 60 minutes, or until a toothpick inserted in the center comes out clean.
Carefully remove the bread from the pan and let it cool on a wire rack. Store the cooled bread in an airtight container for up to 2 days, or freeze it for later.