What would have Numerians coach looked like?

When he was assassinated and hidden in his coach by his father in law Arrius Aper it was said that his corpse was discovered by soldiers breaking into it after noticing a horrible stench. I'm wanting to write a draft for a script that's about Diocletian's reign and should this ever make it anywhere I feel as though it's an important detail to note. At the least a description of a coach from that Era would be nice.