Garv probably has it down, though, I'm just going to ask a few questions.

You meant a gnw week, right? I'm assuming you mean the whole cycle and not just a day due to this being a wednesday.

But, the big question is, did you register? You mention in the title that you didn't qualify despite having registered, you'd need to have 200+ AP to register, as Garv pointed out earlier, but if you got the letter saying your group is due for war (Obtained by having someone register your group for the GNW), and you can prove that it says to do war at X:30 (which I'd presume is 19:30.), for the 20th of June, you should be able to get into it

Edit-If you have 199 or less on all of the 3 days, it's a no-go.