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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+80x^75+186x^76+132x^77+430x^78+282x^79+756x^80+996x^81+678x^82+1416x^83+980x^84+66x^85+66x^86+76x^87+180x^88+36x^89+80x^90+42x^91+24x^92+24x^93+18x^94+4x^96+6x^97+2x^111

The gray image is a linear code over GF(3) with n=369, k=8 and d=225.
This code was found by Heurico 1.16 in 0.154 seconds.