Thanks for this interesting photo Alex! The case is similar to the 4538, but the differences are its sub-seconds dial and movement. So far we know the XXL family includes the ref 4536, 4537, 4538 and 4539, all being 38mm in diameter but differing in lug-to-lug dimensions according to design.
Ref 4538, Antiquorum photo
Ref 4536, author's photo
Ref 4539, Antiquorum photo
Now here is another mystery! This model is similar to the 4539 above, but again with sub-seconds. Any idea what its reference number is? It can't be 4540 according to Antiquorum's reference index, which shows a different and smaller case.