How can I preserve a creamy yogurt for at least two weeks without using any preservatives?
Stored in the refrigerator, homemade yogurt can keep for up to 2 weeks. If you're planning to use it for re-culturing a new batch, you'd want to do that within about a week. You can also put active yogurt in the freezer to save it to culture future batches. For this, one trick is to freeze in small amounts of about a tablespoon each using an ice cube tray (I use a ravioli mold).
Assuming you can manage reasonable sanitation in producing the yogurt, 2 weeks, refrigerated, is not remotely a long time to store it.
This commercial producer states a shelf life of 63 days, but they suggest 7 days once the product has been opened.