Barnabas-Z, also known as BalnabZ, FusedMecha, or Balnab-Z, is a boss in Final Fantasy IV. After being defeated by the party, Barnabas apparently loses his head, which results in Dr. Lugae stepping in to take control of his creation himself. It is possible to miss this boss, if the doctor is defeated first, or quickly after Barnabas.
All one can really do here is attack Barnabas-Z at every opportunity. The damage that is caused when it explodes is equal to however much HP it has left, so at best the player will take it out before it detonates, and at worst one will be minimizing however much damage is caused by the explosion.