Which of the following sentences is grammatically correct?
I being not at home, my friend left a message.
Me being not at home, my friend left a message.
My being not at home, my friend left a message.
I think that the third sentence can be easily ruled out since My being not at home would be a gerund, and we need a participle here.
I have seen sentences like Him being dead, there was no one remaining to challenge her. and I think they are grammatically correct. Following this trend of using the objective case, I believe that the second sentence would be the correct one, but my teacher says that it should be the first one (probably because the second one does have an informal feel to it).
So, which one of them is the correct one, and why?