The generator matrix

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

generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+102x^27+328x^30+546x^33+1144x^36+1910x^39+7128x^42+20892x^45+21030x^48+2628x^51+1808x^54+1010x^57+390x^60+110x^63+22x^66

The gray image is a linear code over GF(3) with n=69, k=10 and d=27.
This code was found by Heurico 1.16 in 13 seconds.