Air carrier pilot departing DFW reported being issued a revised departure procedure while taxiing at DFW that could not be located in any published material. Company dispatch was also unaware of a procedure with this name.

Narrative

Captain and I were on a flight from DFW to ZZZ. We were given the usual route on our flight release with nothing special. However; during our taxi; we were advised to monitor the re-route frequency for there was a change in our flight plan due to weather. The Captain stopped the aircraft; advised tower of our intentions and we began to monitor. This is where the confusion occurred. The ATC worker in the reroute frequency said something along the lines of Aircraft X; amendment to your route … (I don't remember the details) fly the Coda departure then the rest of the route is as filed". The Captain and I spent a few minutes looking for every chart to find a CODA DEPARTURE but was unable to find it anywhere. We asked ATC to confirm it 3-4 times; and all he said was fly the CODA 9 departure; then the rest is as published. We finally said "We are unable to find the CODA 9 departure" the ATC responded "Contact your dispatch …". We contacted dispatch and they were also unaware of the departure. So we returned to ATC to finally ask for the exact fixes on the route; after the 5th time we called about the confusion. He goes to tell us the fixes one by one and to end it with "THEN AS FILED". Captain REPEATED all the fixes back; to which the controller confirmed our read back. After all this; we continued with the flight. During our departure; there was a no error until after the CODA departure we turned to; what we thought was the "AS FILED" portion of our route; but turned out we were flying to an incorrect fix. Forth Worth Center very nicely advised us the correct fix that we were supposed to fly to and we turned to fly to that fix THEN everything went as filed. No further events occurred afterwards. ATC relied on pilots to know where to find the CODA departure. Newer pilots in DFW area aren't aware of the CODA 9 departure that isn't on any charts. Possible read back error on both ends; pilot and ATC - causing possible deviation enroute. The ATC could've been more helpful the 3rd time I had called about the confusion. The pilots had everything in the FMS system to which they thought was correct. Possibly more attention during the read back of the fixes."