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

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+222x^72+216x^75+1458x^76+216x^78+36x^81+36x^90+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 29.3 seconds.