Chiminhtui, which test were you doing? I have looked for the question but couldn't find it and it looks a bit strange with 'am' instead of 'have', and the natural answer would be 'have just finished'. In answer to your question, just can go in various positions depending on what it is modifying:
Just I did it = I was the only one who did it.
I just spoke to him = I spoke to him recently or I only spoke (= I didn't shout, etc)
I am just finished with the homework.
This could mean that you have this minute finished the homework. "Just now." Whew!
It could also mean that it's all you have done so far. You still have to do the dishes.
I just am finished with the homework.
This might mean both, as well, but more likely means you still have to do the dishes.
Thank you so much for answering my question. Yes, this question is on the Beginner-ESL Grammar TEST under Adverds and its Position (or something in that nature). However, under the question of the word "Just," the person who wrote the test forgot to give any examples/multiple choices of the usage of the word "Just" but instead he/she used the word "yet" in the examples.