I thought the Kodet was a single meniscus lens, rather than a doublet? Regardless, do have a look through the lens with the back open just to make sure the lens is clean (if you haven't already checked). Often times lenses on older cameras like this are covered with a layer of dust or haze even though the rest of the camera appears fresh; especially on the inside surface, where the previous owner may not have tried to clean before selling. On some, a good lens cleaning can make a huge difference in the contrast of the images. But in general, my experience with simple-lensed camera is that at f/16 or smaller you should be able to get surprisingly sharp and high-contrast images, so I would guess something is amiss with yours.
For what it's worth, I actually prefer using faster speed films (ISO 400) with cameras like this, just for the sake of being able to work at the smaller apertures.
Good luck with your Tourist!