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

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+384x^72+600x^75+972x^77+78x^78+72x^81+66x^84+12x^87+2x^108

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 0.202 seconds.