The generator matrix

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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+324x^76+504x^77+2150x^78+1242x^79+2232x^80+2984x^81+1500x^82+2064x^83+2866x^84+1074x^85+1152x^86+1108x^87+378x^88+36x^89+36x^90+12x^91+6x^92+2x^93+6x^94+6x^96

The gray image is a linear code over GF(3) with n=369, k=9 and d=228.
This code was found by Heurico 1.16 in 0.49 seconds.