The generator matrix

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

generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+78x^34+96x^35+510x^36+804x^37+594x^38+1438x^39+2166x^40+1644x^41+3126x^42+5340x^43+3288x^44+5260x^45+8532x^46+3984x^47+5590x^48+6636x^49+2676x^50+2868x^51+2304x^52+828x^53+804x^54+384x^55+12x^56+64x^57+18x^60+4x^63

The gray image is a linear code over GF(3) with n=69, k=10 and d=34.
This code was found by Heurico 1.16 in 11.1 seconds.