The generator matrix

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

generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+192x^38+176x^39+756x^41+402x^42+906x^44+594x^45+1320x^47+608x^48+900x^50+336x^51+264x^53+62x^54+36x^56+8x^57

The gray image is a linear code over GF(3) with n=69, k=8 and d=38.
This code was found by Heurico 1.16 in 0.172 seconds.