Preheat the oven to 350° F.

Grate the zucchini with the large holes of a box grater. Set the grated zucchini aside. Dice the strawberries into small bite-sized pieces and set aside.

Add the flour, baking powder, baking soda, and salt to a large mixing bowl, and stir to combine.

To a separate mixing bowl, add the vegetable oil, buttermilk, egg, and vanilla extract. Whisk well for 1-2 minutes to incorporate all the ingredients.

Add the granulated sugar and brown sugar to the wet ingredients. Whisk until the mixture is smooth.

Pour the wet ingredients into the dry ingredients. Use a wooden spoon or spatula to stir until the batter is fully combined, and no dry ingredients remain.

Toss the diced strawberries in a tablespoon of flour. Add the zucchini and strawberries to the batter and fold them in gently.

Line an 8x4 loaf pan with parchment paper. Pour the batter into the prepared pan.

Bake the bread in the preheated oven for 55-60 minutes, until a toothpick inserted into the middle of the bread comes out clean. Allow the bread to cool in the pan for about 5-10 minutes, and then remove to a cooling rack to cool completely.