For the mint lime simple syrup: Place a small saucepot over medium heat. Pour in the sugar, lime juice and 1/2 cup water. Add the mint and simmer until the sugar is dissolved, 3 to 5 minutes. Turn off the heat and cool completely, then remove and discard the mint. This can be stored in airtight container in the refrigerator for up to 2 weeks.
For the cocktail: Fill 4 Collins glasses with ice to chill.
Fill a cocktail shaker with ice, then add the gin, lime juice and 1/4 cup mint lime simple syrup. Shake vigorously and strain over the ice in the chilled Collins glasses. Slowly pour 1/2 teaspoon grenadine on top of each cocktail, then divide the club soda on top of each. Garnish with fresh mint leaves and lime wedges. Serve immediately.