Toss grated papaya with 1/4 cup salt together in a large bowl; allow to sit for 1 hour. Drain liquid from papaya and rinse thoroughly. Place papaya in the middle of a large piece of cheesecloth and squeeze to drain as much liquid from the papaya as possible.
Combine papaya, carrot, bell pepper, chile peppers, ginger, and raisins together in a clean large bowl; mix. Transfer the mixture to clean, dry jars with lids.
Stir vinegar, water, sugar, and 1 teaspoon salt together in a small saucepan; bring to a boil for 5 minutes. Pour the vinegar mixture into the jars, making sure the vegetables are completely submerged in liquid. Allow vegetables to marinate in the liquid at least 1 day before using. Store in the refrigerator between uses.
