You need to interact with the dead girl outside that room. Then, there's a dead zombie on a spike in the previous room, blow that zombie and you'll be able to walk by the invincible zombie.
Do you mean the green zombie or the white zombie? For the white zombie, blow the zombie on the spike a few rooms back. For the green zombie, just keep running to the right and slide past enemies and spikes. Don't stop running and you'll beat the green zombie to a portal.
