The generator matrix

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

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+1092x^71+1814x^72+846x^73+2694x^74+2492x^75+1740x^76+3060x^77+2400x^78+492x^79+1860x^80+970x^81+144x^82+24x^83+10x^84+6x^85+18x^86+6x^87+12x^88+2x^90

The gray image is a linear code over GF(3) with n=342, k=9 and d=213.
This code was found by Heurico 1.16 in 61.1 seconds.