Preheat the oven to 350 degrees F. Grease and flour a 9 by5-inch loaf pan
In a large bowl using an electric mixer cream together the butter, sugar, and lime zest until light and fluffy.
Add the egg and mix in.
Combine the flour, baking powder, baking soda, and salt together.
Add half this combination to the wet ingredients and mix in.
Add the milk and mix until well combined.
Add the remaining flour combination and mix until combined.
Add the berries and fold in, just until they are combined
Pour into the prepared bread pan.
Place into the preheated oven. Bake 55 to 60 minutes, test with a wooden pick, when inserted into the bread when it comes out clean the bread is done.
Glaze-
While the bread is baking combine the lime juice and sugar, stir until the sugar dissolves. Set aside.
Once the bread comes out of the oven pour the lime mixture over the top of the bread.
Set the loaf and a cooling rack for about a half an hour or up to an hour and remove from the bread pan.