The generator matrix
1 1 1 1 1 1 1 1 1
0 X 0 0 X X a*X a^6*X a^6*X
0 0 X 0 a^7*X a^6*X a*X a^7*X a^2*X
0 0 0 X a^7*X X a^5*X X a*X
generates a code of length 9 over F9[X]/(X^2) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+672x^54+864x^63+55296x^72+2216x^81
The gray image is a linear code over GF(9) with n=81, k=5 and d=54.
This code was found by Heurico 1.16 in 0.0592 seconds.