The generator matrix

 1  0  1  1  1  1  1 2X^2  1  1  1  X 2X^2+2X  1 2X^2+X  1  1  1  1  1  1  1  1  1 2X  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  2 2X^2+X 2X^2+X+2 2X^2+2X+1  1 2X 2X+2 X+1  1  1 2X^2+X+2  1  0 2X^2+2X+2 2X^2+2 2X+1 2X  1 2X^2+X X+2  1  1 2X^2+X+1 2X+1  2 X^2+2 X^2+2X+1 2X^2+X+1 2X^2+X+1 X^2+1 2X^2+X+2 2X^2+X+2  2 2X^2+2X+2 2X^2+2X+2
 0  0 2X  0 2X^2 2X^2 2X^2+2X 2X^2+X  0 2X^2 2X  X  X X^2+2X 2X^2 X^2+2X 2X^2+X X^2+X 2X^2+X X^2+2X 2X^2+X 2X^2+2X 2X^2+X X^2+X 2X^2  X  X 2X^2+2X X^2+X 2X^2+2X  X 2X^2+2X X^2+2X 2X^2  0  X X^2+2X  X
 0  0  0 X^2 X^2  0 2X^2 X^2 2X^2 2X^2 X^2  0 2X^2 2X^2 X^2 X^2 2X^2  0 X^2 2X^2  0  0 X^2 2X^2 2X^2 X^2  0 2X^2 X^2  0 2X^2 2X^2 X^2 X^2 X^2 2X^2  0  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+176x^69+342x^70+846x^71+1440x^72+630x^73+1422x^74+4458x^75+978x^76+2430x^77+4414x^78+750x^79+1098x^80+332x^81+108x^82+36x^83+96x^84+84x^85+12x^87+24x^88+4x^96+2x^105

The gray image is a linear code over GF(3) with n=342, k=9 and d=207.
This code was found by Heurico 1.16 in 0.621 seconds.