The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+78x^69+156x^70+120x^71+372x^72+264x^73+624x^74+816x^75+1692x^76+1080x^77+724x^78+156x^79+42x^80+86x^81+78x^82+60x^83+66x^84+72x^85+18x^86+42x^87+12x^88+2x^105

The gray image is a linear code over GF(3) with n=342, k=8 and d=207.
This code was found by Heurico 1.16 in 0.137 seconds.