The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+176x^81+78x^82+180x^83+276x^84+126x^85+66x^86+272x^87+138x^88+84x^89+194x^90+66x^91+72x^92+118x^93+36x^94+60x^95+112x^96+24x^97+24x^98+38x^99+18x^100+26x^102+2x^108

The gray image is a linear code over GF(3) with n=132, k=7 and d=81.
This code was found by Heurico 1.13 in 0.0313 seconds.