The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+56x^78+102x^79+300x^80+302x^81+264x^82+570x^83+500x^84+240x^85+516x^86+366x^87+282x^88+588x^89+338x^90+258x^91+432x^92+326x^93+156x^94+384x^95+200x^96+120x^97+120x^98+68x^99+36x^100+6x^101+20x^102+6x^105+2x^108+2x^114

The gray image is a linear code over GF(3) with n=132, k=8 and d=78.
This code was found by Heurico 1.16 in 0.399 seconds.