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

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+426x^68+324x^69+738x^71+420x^72+1020x^74+506x^75+804x^77+366x^78+690x^80+314x^81+474x^83+212x^84+210x^86+30x^87+12x^89+12x^90+2x^93

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 99.5 seconds.