The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+180x^74+230x^75+450x^76+816x^77+1068x^78+1194x^79+2004x^80+1942x^81+2016x^82+2832x^83+2902x^84+2910x^85+3852x^86+4136x^87+3732x^88+4566x^89+4098x^90+3546x^91+4218x^92+3296x^93+2442x^94+2262x^95+1342x^96+960x^97+900x^98+592x^99+216x^100+240x^101+52x^102+30x^103+22x^105+2x^123

The gray image is a linear code over GF(3) with n=132, k=10 and d=74.
This code was found by Heurico 1.16 in 35.3 seconds.