The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+456x^77+342x^78+1278x^80+846x^81+1884x^83+1044x^84+2454x^86+1044x^87+2502x^89+1452x^90+2448x^92+1206x^93+1386x^95+462x^96+576x^98+114x^99+132x^101+36x^102+6x^104+6x^105+8x^108

The gray image is a linear code over GF(3) with n=132, k=9 and d=77.
This code was found by Heurico 1.16 in 30.4 seconds.