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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+96x^72+214x^75+486x^80+86x^81+4374x^82+972x^83+138x^84+42x^90+112x^93+18x^99+20x^102+2x^120

The gray image is a linear code over GF(3) with n=369, k=8 and d=216.
This code was found by Heurico 1.16 in 18.6 seconds.