The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+174x^79+282x^80+236x^81+396x^82+450x^83+382x^84+504x^85+504x^86+348x^87+420x^88+408x^89+278x^90+396x^91+336x^92+260x^93+276x^94+270x^95+132x^96+198x^97+156x^98+64x^99+54x^100+24x^101+12x^103

The gray image is a linear code over GF(3) with n=132, k=8 and d=79.
This code was found by Heurico 1.16 in 0.438 seconds.