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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+274x^72+126x^73+216x^74+264x^75+396x^76+432x^77+198x^78+126x^79+104x^81+24x^84+18x^87+6x^90+2x^99

The gray image is a linear code over GF(3) with n=342, k=7 and d=216.
This code was found by Heurico 1.16 in 0.0427 seconds.