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.