The generator matrix

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

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+78x^72+30x^74+204x^75+354x^77+364x^78+762x^80+636x^81+1764x^83+936x^84+2874x^86+1156x^87+3300x^89+1348x^90+2556x^92+946x^93+1146x^95+466x^96+312x^98+202x^99+24x^101+118x^102+66x^105+30x^108+10x^111

The gray image is a linear code over GF(3) with n=132, k=9 and d=72.
This code was found by Heurico 1.16 in 4.09 seconds.