The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 X 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2X+1 2 2 1 0 0 2 0 0
0 0 2X 0 0 0 0 0 0 2X X 0 0 2X X X 2X 2X X 0 0 0
0 0 0 X 0 0 0 0 0 2X 2X X X 0 2X 0 2X X 0 2X X 0
0 0 0 0 X 0 0 0 X 2X 2X 2X X 0 X 2X 0 X X 0 X 0
0 0 0 0 0 2X 0 0 2X 2X 0 2X X 2X 0 X 2X X X 2X 0 0
0 0 0 0 0 0 X 0 X 2X 0 0 X 0 2X X 2X 2X 0 X 0 0
0 0 0 0 0 0 0 X X X X X 0 X X 0 0 2X X 2X 0 X
generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.
Homogenous weight enumerator: w(x)=1x^0+46x^27+6x^28+182x^30+24x^31+470x^33+312x^34+972x^36+2040x^37+2464x^39+6540x^40+4548x^42+12120x^43+5088x^45+12372x^46+3852x^48+5424x^49+1410x^51+528x^52+442x^54+142x^57+52x^60+12x^63+2x^66
The gray image is a linear code over GF(3) with n=66, k=10 and d=27.
This code was found by Heurico 1.16 in 7.9 seconds.