Toss the grated papaya with 1/4 cup salt together in a large bowl; allow to sit for 1 hour. Drain the liquid from the papaya and rinse thoroughly. Place the papaya in the middle of a large piece of cheesecloth and squeeze to drain as much liquid from the papaya as possible.
Combine the papaya, carrot, red bell pepper, ginger, green chile peppers, and raisins together in a clean large bowl; mix. Transfer the mixture to clean, dry jars with lids.
Stir the 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 the vegetables to marinate in the liquid at least 1 day before using. Store in refrigerator between uses.