The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 0 X+1 1 2 2X+1 X 0 2 X X+2 2X+1
0 0 2X 0 0 0 0 0 0 0 2X 2X 2X X 2X X X 2X X X X 2X 0
0 0 0 X 0 0 0 X 2X X X 0 2X 2X 0 X X X X X 2X X 2X
0 0 0 0 X 0 X X X X 2X 2X 0 X 0 X X X 2X 2X 0 0 X
0 0 0 0 0 2X 2X 0 2X X 2X 0 X X 2X 2X 0 2X X 0 2X 0 X
generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+72x^36+60x^37+114x^38+100x^39+222x^40+276x^41+120x^42+672x^43+834x^44+104x^45+912x^46+1020x^47+96x^48+804x^49+588x^50+96x^51+246x^52+84x^53+82x^54+36x^57+18x^60+2x^63+2x^66
The gray image is a linear code over GF(3) with n=69, k=8 and d=36.
This code was found by Heurico 1.16 in 0.209 seconds.