Ooh, creepy! Are you sure a cat couldn't have sneaked in? My sister had no cats, but they always used to find a way to get in her house and poo everywhere!
Possibility of it being put there by :
a) a pixie or small elf (not the 'pixie' of lit of course)
b) your god as a punishment
c) or it is a growth of the carpet
However these are only ideas and I suggest you investigate the case throroughly - keeping a record of notes!
Probably tracked in on the side of a shoe, sat unnoticed overnight or longer. You weren't at the computer for a couple of weeks? How long since in the room at all?