Combine tonic water and sugar in a small saucepan and bring to a boil over medium-high heat. Boil for 2 minutes and remove from heat. Stir in gin and let cool while you assemble the ice pops.
Cut lime into 6 slices. Cut each slice in half. Place 2 pieces of lime in each mold. Evenly divide berries among the molds.
Pour tonic water mixture into the molds through a funnel, leaving a 1/2-inch space on the top. Freeze for 8 hours, or overnight.