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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+68x^72+172x^75+18x^76+214x^78+36x^79+252x^81+360x^82+230x^84+1080x^85+246x^87+1260x^88+216x^90+1260x^91+224x^93+360x^94+172x^96+154x^99+124x^102+66x^105+38x^108+6x^111+4x^114

The gray image is a linear code over GF(3) with n=132, k=8 and d=72.
This code was found by Heurico 1.16 in 0.749 seconds.