Bring the sugar and water to the boil over high heat. Boil until the sugar has dissolved, then stir in the strawberries, mint, ginger, lemon peels and lemon juice. Return to the boil, then reduce heat to medium and simmer for 20 minutes. Remove from heat, and stir in the white balsamic vinegar.
Allow the syrup to stand overnight at room temperature, then strain out the fruits with a fine sieve. Store at room temperature in a sterile container.
To use, stir 1 part syrup into 4 to 6 parts water; serve cold with ice if desired.