The generator matrix

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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+28x^72+18x^73+6x^74+68x^75+216x^76+228x^77+270x^78+828x^79+1122x^80+1390x^81+3354x^82+4476x^83+3982x^84+8940x^85+8010x^86+5260x^87+9264x^88+5790x^89+2650x^90+1854x^91+702x^92+54x^93+240x^94+78x^95+54x^96+60x^97+36x^99+12x^100+34x^102+12x^105+8x^108+2x^111+2x^114

The gray image is a linear code over GF(3) with n=387, k=10 and d=216.
This code was found by Heurico 1.16 in 5.77 seconds.