Just to add some extra detail to Eddie's reply...
It may be possible to find a drum/percussion BANK that includes the specific sound you're seeking, in which case your midi file can select that BANK. Or, if you find a discreet sound/sample, then that can be selected, maybe using BANK select as well as Program Change. More complicated, you can always find a similar sound and, depending on the nature of the sound, edit/modify that sound, and save the result as your own version.
Whatever you do, as soon as you use that sound in your own composition, your file ceases to be GM compatible, and anyone trying to play the midi file will NOT hear this instrument, unless they have the same sound data loaded, or are using the same external unit. This loses the whole point of the GM soundset. Yes, it is a 'limitation' being restricted to the sounds/instruments on the GM list, but sticking to the list makes many/various devices/systems compatible so that your composition will work, more or less, for anyone.
Is there no way you can replicate the instrument you desire using existing sounds, maybe using two or more existing sounds layered (played overlapped)? May not be perfect, but it would keep your composition GM and allow it to be played by others. Even using two identical sounds, but with different effects/controllers applied to each, might be a help. Always worth experimenting.
Geoff