I agree 100% with the replies.
CW - what you call Morse Code, but actually ham radio uses International Morse Code - which is different than telegraphers Morse code - like what you see on an old western movies with telephone poles and batteries and a key on a desk.
The reason why YOU can’t do morse code on GMRS is because your radio is FM - Frequency Modulation.
Morse Code - CW - Ham Radio, uses a form of Amplitude Modulation where the key turns on and off the transmitter carrier in such a way that it produces a tone. The receiver on the other end receives the tone. The user uses their ears to hear the tone and decipher it into letters and numbers and punctuation etc.
The benefit to using cw is that it is more efficient, because the signal it produces is very narrow and it funnels all the transmitted power into that tone. SSB - Single Side Band, where you basically suppress one of the side bands and maybe even the carrier is a phone version of Amplitude Modulation. Single Side Band is more efficient.
Amplitude Modulation - the transmitter produces a carrier and two side bands. The receiver only uses one of the side bands, throws the other away. The carrier robs half or more of the power produces, yet it does no work. So its wasted power.
so you see, GMRS is a economical way for a person with no knowledge of radio or how it works to communicate locally, while Ham Radio is a more expensive version of radio both in terms of knowledge, time invested in learning the theory and taking multiple exams to obtain the licenses necessary to gain the privileges you desire. And the equipment, since most good amateur radio HF equipment would probably put you back $1500 or more, by the time you bought the radio, power supply, antenna, swr meter, dummy load, speaker, tower, coax, extra microphones and all other peripheral devices hams uses today , even computers used to communicate digitally with other hams all over the world. You can easily spend $8000 just on a good HF transceiver, $5,000 just on an entry level beam antenna set up.
If this sounds appealing to you, maybe you ought to look closer to amateur radio than GMRS, maybe you would make a good ham.