Preheat your oven to 350°F (175°C). Grease a loaf pan.
In a mixing bowl, whisk together flour, baking powder, baking soda, and salt.
In another bowl, beat the eggs, then add sugar, oil, lemon zest, and vanilla extract. Mix well.
Stir in the grated zucchini.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Pour the batter into the prepared loaf pan.
Bake for 50 minutes, or until a toothpick inserted into the center comes out clean.
Let the bread cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.