The generator matrix

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

generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+282x^67+358x^69+618x^70+396x^72+852x^73+414x^75+822x^76+496x^78+936x^79+316x^81+624x^82+126x^84+210x^85+58x^87+30x^88+14x^90+6x^96+2x^99

The gray image is a linear code over GF(3) with n=114, k=8 and d=67.
This code was found by Heurico 1.16 in 56.8 seconds.