The generator matrix

 1  0  1  1  1  1
 0  1  1  a a^7*X+a^2  0
 0  0 a^7*X  0 a^7*X  X
 0  0  0  X a^7*X a^7*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+648x^32+720x^36+23328x^40+10368x^41+2448x^45+262440x^48+186624x^49+41472x^50+3232x^54

The gray image is a linear code over GF(9) with n=54, k=6 and d=27.
This code was found by Heurico 1.16 in 0.746 seconds.