The generator matrix

 1  0  1  1  1  1  1  0  1  0  1  1  1  1  1  0  X  1  1  1  0  1  1  X  1  1  X  1  1  0  1  1  1  1  1  1  X  1  1  X  1  1  1  X
 0  1  1  2  0  1  2  1 2X+1  1  0  2 X+2 2X+1  0  1  1  0  2 2X+1  1  2 2X+1  1 2X+1  2  1  1 2X+1  1 X+1  X X+2 X+1 X+1 2X+2  1  1  X  0  2 2X+2 2X+2 2X
 0  0 2X  0  0  0  0  0  0  0 2X  X  X 2X 2X 2X 2X 2X 2X  0  X  X  0  0 2X 2X 2X  0  X 2X  X 2X  X  X  0 2X 2X  X  0  X  X 2X  X  X
 0  0  0  X  0  0  0  X 2X  X  0 2X  X 2X 2X  0 2X 2X  0  X 2X  X 2X  X  X 2X  X 2X  X  X 2X 2X  X 2X  X 2X  X 2X 2X 2X 2X  X  X  X
 0  0  0  0  X  0  X  X  X  X  X 2X  0  X  X  0 2X  0  0  0  0 2X 2X 2X  X 2X  0  X  X 2X  0  X  0 2X  X  0 2X  X  0  0  0  X 2X 2X
 0  0  0  0  0 2X 2X  0 2X  X  0 2X  X  X 2X 2X  X  X 2X 2X  0  0  X  0  0 2X 2X  X  0 2X 2X  0  0 2X 2X 2X  X  X  X  0  0  0 2X 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+78x^76+252x^78+210x^79+276x^81+510x^82+216x^84+864x^85+456x^87+990x^88+360x^90+858x^91+270x^93+672x^94+210x^96+150x^97+78x^99+36x^100+6x^103+48x^105+14x^108+6x^114

The gray image is a linear code over GF(3) with n=132, k=8 and d=76.
This code was found by Heurico 1.16 in 70.6 seconds.