The terminology “ground mode “ is not a typical term in the industry . What ATC wants is for your transponder to be operating with ALT ON + TCAS OFF . Depends on the airplane , you may have the following ( STBY, ALT OFF, ALT ON, TA ONLY , TA/RA ,AUTO ) on your ATC/TCAS control panel, or other device to control the transponder and the TCAS. Just select ALT ON, or AUTO (Auto is typically designed to turn the TCAS on or off based on weight on wheel status ) and you’d be good. ATC needs a working transponder to enable the detection of airplanes on ground at most major airports with surface movement detection such as the ASDE-X which can use different techniques to track airplane including ADS-B OUT which will be working in any position other than STBY.
note : ALL MODE S ARE INHIBITED from replying to a mode s all call, which is what SSR (ATC ) uses to acquire airplanes flying around and put them on the roll call for future individual mode s interrogations.