Preheat your oven to 350°F (175°C). Grease a 9x5 inch loaf pan.
In a large bowl, whisk together the flour, baking soda, cinnamon, and salt.
In another bowl, beat the eggs, honey, yogurt, and vanilla extract until well combined.
Stir the wet ingredients into the dry ingredients until just combined. Do not overmix.
Fold in the shredded zucchini and chopped walnuts.
Pour the batter into the prepared loaf pan and smooth the top.
Bake for 55-60 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.