Preheat the oven to 350°F (175°C) and grease a loaf pan.

In a mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

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

Gradually add the dry ingredients to the wet mixture, alternating with the buttermilk. Mix until just combined.

Fold in the mashed blackberries, lemon zest, and lemon juice.

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

Bake for 50-55 minutes, or until a toothpick inserted in 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.

In a small bowl, whisk together the powdered sugar and lemon juice until smooth.

Drizzle the glaze over the cooled loaf cake before slicing and serving.