The generator matrix
1 1 1 1 1 1
0 X 0 0 X X
0 0 X 0 a^7*X a^6*X
0 0 0 X a^7*X X
generates a code of length 6 over F9[X]/(X^2) who´s minimum homogenous weight is 27.
Homogenous weight enumerator: w(x)=1x^0+160x^27+720x^36+2448x^45+52488x^48+3232x^54
The gray image is a linear code over GF(9) with n=54, k=5 and d=27.
This code was found by Heurico 1.16 in 0.0253 seconds.