The generator matrix

 1  1  1  1  1  1  1  1
 0  X  0 X^2 2X 2X^2+X X^2 2X^2+2X
 0  0  X 2X^2+2X X^2 2X^2+2X X^2 2X^2+X

generates a code of length 8 over Z3[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+60x^12+36x^13+90x^14+148x^15+1548x^16+36x^17+194x^18+36x^19+36x^20+2x^24

The gray image is a linear code over GF(3) with n=72, k=7 and d=36.
This code was found by Heurico 1.16 in 0.00189 seconds.