The generator matrix

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

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+146x^12+972x^14+536x^15+2430x^16+1944x^17+512x^18+16x^21+4x^24

The gray image is a linear code over GF(3) with n=72, k=8 and d=36.
This code was found by Heurico 1.16 in 0.00731 seconds.