The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+120x^76+240x^77+120x^78+822x^79+870x^80+254x^81+996x^82+1308x^83+414x^84+1380x^85+1614x^86+432x^87+1776x^88+1692x^89+358x^90+1770x^91+1632x^92+294x^93+1236x^94+990x^95+218x^96+534x^97+336x^98+70x^99+96x^100+66x^101+12x^102+18x^103+2x^105+10x^108+2x^114

The gray image is a linear code over GF(3) with n=132, k=9 and d=76.
This code was found by Heurico 1.16 in 4.41 seconds.