The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+106x^72+48x^73+186x^74+458x^75+270x^76+984x^77+1018x^78+804x^79+1860x^80+1736x^81+1308x^82+3330x^83+2928x^84+2316x^85+5046x^86+4156x^87+3072x^88+6288x^89+3862x^90+2892x^91+4986x^92+2988x^93+1614x^94+2490x^95+1614x^96+660x^97+870x^98+548x^99+126x^100+192x^101+148x^102+12x^103+12x^104+68x^105+36x^108+12x^111+2x^114+2x^117

The gray image is a linear code over GF(3) with n=132, k=10 and d=72.
This code was found by Heurico 1.16 in 28.8 seconds.