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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+38x^72+18x^74+52x^75+108x^77+52x^78+216x^80+34x^81+144x^83+10x^84+16x^87+20x^90+6x^93+4x^96+6x^99+2x^102+2x^111

The gray image is a linear code over GF(3) with n=120, k=6 and d=72.
This code was found by Heurico 1.16 in 0.015 seconds.