In a saucepan, combine sugar and 2 cups of water, then heat on high for two minutes until all granules have melted. Set aside to cool.
Rinse the berries then place in a pitcher or bowl and muddle until you've extracted as much juice as possible. (Alternatively you can pulse in the blender.)
Add to this the lemon and lime juice and pulse a couple of times to combine.
Pour the juice in to a large pitcher through a mesh strainer to catch any seeds and excess pulp.
Then, add the simple syrup and additional water. Stir well.
Serve over ice with a couple of leaves of fresh basil and a little lemon zest.
Optional, rim the glass in sugar and lemon zest.