The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+402x^67+816x^68+2076x^69+3894x^70+5526x^71+9780x^72+11472x^73+15678x^74+21174x^75+24624x^76+25362x^77+23586x^78+15690x^79+8796x^80+5108x^81+1992x^82+630x^83+156x^84+192x^85+48x^86+78x^87+54x^88+6x^89+6x^90

The gray image is a linear code over GF(3) with n=342, k=11 and d=201.
This code was found by Heurico 1.16 in 34.5 seconds.