The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+156x^70+222x^71+332x^72+786x^73+318x^74+778x^75+1308x^76+486x^77+828x^78+906x^79+228x^80+76x^81+60x^82+24x^83+24x^85+18x^86+6x^87+2x^93+2x^99

The gray image is a linear code over GF(3) with n=342, k=8 and d=210.
This code was found by Heurico 1.16 in 0.0825 seconds.