The generator matrix

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

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+98x^12+276x^14+80x^15+972x^16+528x^17+218x^18+6x^20+4x^21+4x^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 0.0012 seconds.