I dimly recall that the ground wire on the passenger side of the car, ran to one of the bolts that held the p.s. fluid reservoir, or one on the alternator brackets. So its a block-to-body ground I think. And yes, having the block be at the same ground potential as the negative side of the battery is probably necessary.
If there is another wire like that one on the driver's side of the car, see if it doesnt provide a 'ground' point for the PCM - which is mounted on the inner fender wall of the engine compartment, partly hidden under the outer fender.
Our 97 Neon SHC has the same code showing up. It also 'hiccups' now and then, most notably about the time you are on a long bridge or highway flyover -with-no-shoulder-at-all. It has been doing this for a year now, but it has stayed running so far. I say it 'hiccups', because its not like one cylinder is misfring - its more violent than that. It feels like all 4 cylinders dont fire. Its very brief, but everyone in the car notices it. My 5 year old grandson says the car is sneezing.