The generator matrix

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

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+150x^12+54x^13+792x^14+510x^15+2970x^16+1440x^17+548x^18+54x^19+36x^20+6x^21

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 0.00802 seconds.