Add peeled kiwi fruit, lime juice, and simple syrup to a blender. Blend until smooth.
Add kiwi mixture, gin, and ice cubes to the cocktail shaker. Shake vigorously for at least 5 seconds.
Using a cocktail strainer, strain the drink into the glass. The kiwi mixture will be thick, so you might need to shake it a few times to pour out all the liquid.
Top with carbonated mineral water and serve.
Notes
If you want less pulp or almost no pulp, use a mesh while pouring the kiwi mixture into the glass.
Since the kiwi mixture will be thick, use ice cubes instead of crushed ice. It will be challenging to strain the cocktail otherwise.