The generator matrix

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

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+210x^38+214x^39+624x^41+422x^42+1002x^44+522x^45+1356x^47+598x^48+942x^50+338x^51+240x^53+62x^54+16x^57+14x^60

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 6.84 seconds.