The generator matrix

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

generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+402x^68+330x^69+792x^71+396x^72+972x^74+528x^75+834x^77+390x^78+702x^80+266x^81+432x^83+228x^84+222x^86+36x^87+18x^89+12x^90

The gray image is a linear code over GF(3) with n=114, k=8 and d=68.
This code was found by Heurico 1.16 in 19 seconds.