My carrier gas furnace is reading code 13 I had to install a return to a new furnace and keep getting code 13

Sometimes you need to watch the codes carefully. There will be a different time spacing between 13 and 31. The first digit is the number of short flashes, the second digit is the number of long flashes.
13 is a limit lockout, typically high limit.
31 is the pressure switch didn't close or reopened.
13 is usually from air restriction in the return or through the filters, look for dirty filters or collapsed return lines.
31 can be a blocked flue, dirty orifice on the pressure switch, disconnected hose from the inducer to the switch or a bad switch. I have seen small slits in the inducer line cause the shut down.