The generator matrix

 1  0  0  1  1  1  1  1
 0  1  0 2X^2+2X  1 2X^2+2X+1 2X^2+X 2X^2+X+1
 0  0  1 2X^2+2X+1  1 2X^2+2X 2X^2+X+1 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+634x^12+1944x^14+2352x^15+8586x^16+3672x^17+2432x^18+54x^20+8x^21

The gray image is a linear code over GF(3) with n=72, k=9 and d=36.
This code was found by Heurico 1.16 in 0.0536 seconds.