Others here will know best, but I don't think you need to run the engine to get the codes. I've never had to do it, but I'd guess just putting the ignition to "On" and lighting up the dash should give you access to the codes.
I'd also reconsider starting up the engine regularly while in storage. Unless you're getting it up to full highway temperature, that practice can be more harm than good.
You might check your coolant expansion tank as an easy first move. Low coolant, below the sensor in the tank, is a common cause of the engine problem lamps. If it does prove low, look for hose and fitting leaks, or cracks in the tank or around its fittings.
Joel