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  0  0  0  0  0  0  0  0  X 2X 2X  X  X  X  0 2X 2X  X  X  X 2X  0  0 2X  X 2X  X  X  X  0  0  X  X  0 2X  0 2X 2X 2X
 0  0  X  0  0  0  0  X 2X 2X 2X  0  0 2X  X 2X  X  0  X  X  X  0  0 2X 2X 2X 2X 2X  0 2X  0  X  X  X  0 2X 2X  0  0  0  X
 0  0  0  X  0  0  X 2X  0 2X  0  0 2X  X  X 2X  0  X 2X 2X 2X  X  0 2X 2X  X 2X  0 2X 2X  X 2X  X  X  X  X  X 2X  0  X  0
 0  0  0  0  X  0 2X 2X  X  0 2X 2X 2X  0 2X 2X  0 2X 2X  X  0  0  0 2X 2X  X 2X 2X  0  0  X  0 2X 2X 2X  X 2X  0  X 2X  0
 0  0  0  0  0  X 2X 2X 2X 2X 2X 2X  X 2X  X  X 2X  X  0 2X 2X  0  X  X 2X  0 2X  0  X  X  X  X  X 2X 2X  X 2X  X 2X  0 2X

generates a code of length 41 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+96x^72+214x^75+486x^80+86x^81+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=123, k=7 and d=72.
This code was found by Heurico 1.16 in 4.92 seconds.