The generator matrix

 1  0  0  0  0  1  1  1  1  1  1 2X  0  X  1  1  1 2X  1  1  0  X  0  1  1  1  1  1  1  1  0  1  1  1  1  1  X  1  1  1  0  1 2X  1
 0  1  0  0  0  0  X  1 2X+1 2X+2  2  1  X  1  1 2X+2  1  1  2 X+2  0  1  1 2X+1 X+1 X+1 2X 2X 2X+1 X+1  0  X 2X 2X X+2  2  X  0 2X+2 2X+2  1  X  1  0
 0  0  1  0  0  0 2X+1  X 2X+2 X+1  2 X+1  1 2X+2 2X+1  X  1 2X X+1 X+1  1 X+1 X+1 2X+1 X+2 X+2 X+1  2  1  2  1 X+1  0  X 2X+2  0  1 X+1  1  1 X+1 X+1  2  X
 0  0  0  1  0  1 2X+1 X+1 X+1 2X+1  1 2X 2X+2  1  X X+2 X+2  2  X  0 2X 2X+1 2X+2 X+1  1  0  2  1  X 2X 2X+2 X+1  0 2X+2 X+2  1  1 2X  X X+2 2X+2  X 2X+1  0
 0  0  0  0  1  2 2X  0  1 X+1 2X+2 2X+2 X+2  0  0  1 2X 2X+2 2X 2X+2 2X+1  X  1 X+2  X X+2 X+2 2X+2 X+1  0  1 2X+1 X+1 2X+1 2X+1 X+1  X  2 2X+1  2 2X+2 X+1 X+2 2X
 0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  X 2X  0  X  X 2X 2X  X 2X  X  0  0  0 2X  0  X  X 2X  0  0  X  0  X  0  0  X  0 2X  X  X  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+126x^72+384x^73+594x^74+1274x^75+1404x^76+1938x^77+3260x^78+3024x^79+3930x^80+6686x^81+5664x^82+6900x^83+11274x^84+9138x^85+10068x^86+14638x^87+11574x^88+11412x^89+15624x^90+10416x^91+9594x^92+11808x^93+7104x^94+5436x^95+5450x^96+2826x^97+2100x^98+1620x^99+816x^100+462x^101+340x^102+120x^103+54x^104+48x^105+18x^106+12x^108+4x^114+6x^117

The gray image is a linear code over GF(3) with n=132, k=11 and d=72.
This code was found by Heurico 1.16 in 293 seconds.