The generator matrix
1 0 1 1 1 1
0 1 1 a a^7*X+a^2 a^7*X+2
0 0 a^7*X a*X a^6*X a^5*X
generates a code of length 6 over F9[X]/(X^2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+120x^36+3888x^40+240x^45+23328x^48+31104x^49+368x^54
The gray image is a linear code over GF(9) with n=54, k=5 and d=36.
This code was found by Heurico 1.16 in 0.0144 seconds.