By sheer kismet, I ran across one such language yesterday – the Caucasian language Abkhaz. Check out the second row of the Cyrillic script section. See also the Phonology/Consonants section of the article.
It looks like sister Caucasian language Adyghe also contrasts /ʐ/ and /ʒ/. As you’re aware, if one is looking for a language to make Ginsu-fine distinctions between consonants, the Caucasus is a good place to look.
The consonants of Northwest Caucasian are formidable, while the vowels are reduced to a mere vestige. NWC makes full use of every articulation point plus the full range of secondary articulations to multiply the consonant inventory. Only some Khoisan languages exceed the number of consonants, and that’s only because they add a set of clicks as primary and secondary articulations.
I have this vague recollection of pronouncing it “parmezhano”, and by pronouncing, I mean mostly in my mind, as I don’t recall having any reason to say it out loud. I’m pretty sure I must have heard it pronounced that way in a tv commercial, and when people said it correctly I secretly thought they were wrong.