How can I save tomatoes for at least 20 days?
Tomatoes can last that long in a root celar at 15 degrees Celsius. You have to choose tomatoes bred for lasting - so supermarket ones, not homegrown heirloom varieties, and preferably not perfectly ripe and juicy. Your biggest problem would be mold, so carefully check each tomato for places where the skin is torn or the tomato has been squished. Then carefully order them such that there is enough air/ventilation around them, ideally in a single layer. If the humidity around a tomato gets too high, it will grow mold at the place where it grew out of the wine. And never let the temperature drop below 13 Celsius (so don't do it in the fridge!) because they change their taste then. 

If you cannot do that - for example, if you just harvested a large amount of overripe tomatoes and wonder how to not lose them - your only option may be making something out of them that can be canned.