Preheat the oven to 350?F (175?C). Grease and flour a loaf pan.

In a mixing bowl, whisk together the flour, baking powder, baking soda, and salt.

In another bowl, cream the softened butter and sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla, lemon zest, and lemon juice.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Gently fold in the blackberries.

Pour the batter into the prepared loaf pan and smooth the top.

Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.