In a large saucepan, heat 2 cups water and the sugar over medium high heat, stirring until the sugar dissolves. Add the ginger and bring the water to a boil; boil until the syrup reduces slightly, about 5 minutes. Strain and refrigerate.
Fill a tall glass three-quarters full with ice cubes and 3 lime slices. Add one quarter of the chilled ginger syrup, 1/2 cup club soda and 1 ounce gin and stir. Repeat with the remaining drinks.