The generator matrix

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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+64x^75+138x^78+54x^80+108x^81+324x^83+108x^84+5022x^86+62x^87+432x^89+52x^90+64x^93+50x^96+22x^99+26x^102+20x^105+6x^108+6x^111+2x^120

The gray image is a linear code over GF(3) with n=387, k=8 and d=225.
This code was found by Heurico 1.16 in 0.247 seconds.