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Trying to find them using brute force isn't that bad. The following worked for me

import itertools
Z9=Zmod(9)
I=Matrix(Z9,[[1,0],[0,1]])
L=[]
for a,b,c,d in itertools.product(Z9,repeat=4):
    M=Matrix(Z9,[[a,b],[c,d]])
    if I==M^3:
        L.append(M)

The length of the list seems to be 297 though, but the 39th element seems to be the one that was missing from your list.