Well, the only time i can be fully available is on the weekends. However, this weekend i am extremely busy helping others with AF fights, dynamis, quests, etc. From what i've experienced, Z4 can take a long time to complete. It is a pain in the butt.
Z4 fight is a BCNM fight, so you can only have 6 people in there at once. There are 3 tonberries that you need to kill. I forget the classes, its been a while. Thrillagorilla will know, he did it recently.
The party setup should be WHM, BLM, BRD/RDM, TANK, DRK, RNG or another BLM. When i did it, i had a 73 SMN with us, and he soloed 1 of the 3 tonberries himself, but we will not have that luxury this time.