1) the tuesday of the upcoming week
2) the tuesday after the upcoming tuesday
*note only one of these definitions is correct, but nobody knows for sure which one.
We were sittin' in the back of the class, gettin' our drink on, when Billy casually mentioned that he wouldn't be able to attend Donato's on tuesday week. Instead of explaining what that meant, he asked the teacher to explain it. The students responded with boos.