The generator matrix

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

generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+132x^69+84x^70+138x^71+316x^72+138x^73+114x^74+266x^75+96x^76+102x^77+192x^78+78x^79+60x^80+144x^81+60x^82+48x^83+136x^84+12x^85+24x^86+24x^87+18x^88+2x^90+2x^99

The gray image is a linear code over GF(3) with n=114, k=7 and d=69.
This code was found by Heurico 1.13 in 0.024 seconds.