The generator matrix

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

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+260x^75+216x^76+1086x^77+1328x^78+792x^79+1626x^80+3694x^81+1308x^82+2748x^83+3560x^84+972x^85+1236x^86+498x^87+90x^88+48x^89+86x^90+24x^91+42x^92+44x^93+18x^95+2x^96+2x^105+2x^108

The gray image is a linear code over GF(3) with n=369, k=9 and d=225.
This code was found by Heurico 1.16 in 4.28 seconds.