The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+120x^11+92x^12+396x^14+320x^15+792x^17+296x^18+150x^20+16x^21+4x^24

The gray image is a linear code over GF(3) with n=24, k=7 and d=11.
This code was found by Heurico 1.16 in 0.00818 seconds.