The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+234x^71+294x^72+870x^73+792x^74+588x^75+1194x^76+588x^77+532x^78+846x^79+450x^80+92x^81+24x^83+22x^84+12x^86+2x^87+6x^88+6x^89+6x^90+2x^93

The gray image is a linear code over GF(3) with n=342, k=8 and d=213.
This code was found by Heurico 1.16 in 0.077 seconds.