Ah, I saw this one before. The anime is call Gakkou Gurashi.

It's typical slice-of-life anime crap, with a bit of plot (fan-service) and justice (lots and lots of loli subtext). The story is mainly centered around the protagonist in her "awkward period" and her weird fixation on the new transfer student(girl with the shovel). I'm pretty sure it's yuri, but there's also a school teacher (male) in the mix so…

Anyways, there's no real story to this. Just the character forms a club, stuff happens, and all the character react with hilarious hijinks. That's about it. Think Lucky Star crossed with Haruhi.

I don't recommend it at all, unless you like that genre. And no, there is no real zombies in this show. That would have made this a lot easier to watch.