The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+96x^73+180x^74+8x^75+84x^76+216x^77+10x^78+84x^79+36x^80+2x^81+6x^82+4x^84+2x^87

The gray image is a linear code over GF(3) with n=342, k=6 and d=219.
This code was found by Heurico 1.16 in 0.0228 seconds.