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.