The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  0  1 2X^2+X  1  1  1  1  1  1 2X  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1  1 X+1 2X^2+X  1 2X^2+2X+1  1  2  0 2X 2X^2+X+2 2X^2+1 2X+2  1  0 2X 2X^2+2X+1 2X^2+X+2  1 X^2 X^2+2X X^2+2X X^2+2X+1 X+1 X^2+X+1 X^2+2X+1 2X^2+1 X^2+X+1 2X  2 X^2+2
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 2X^2  0 2X^2 X^2 X^2  0 2X^2 X^2 2X^2  0 X^2 X^2 2X^2  0 2X^2 2X^2 X^2 X^2 2X^2 X^2  0  0 2X^2 2X^2 X^2  0  0 2X^2
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 X^2 2X^2 X^2  0 2X^2 X^2 2X^2 X^2  0 2X^2 X^2  0 2X^2 2X^2 2X^2 2X^2  0 2X^2  0 X^2  0 X^2  0 2X^2  0  0 X^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+120x^76+234x^77+508x^78+606x^79+288x^80+1106x^81+828x^82+510x^83+1256x^84+600x^85+216x^86+118x^87+96x^88+36x^89+18x^91+12x^92+2x^93+4x^96+2x^102

The gray image is a linear code over GF(3) with n=369, k=8 and d=228.
This code was found by Heurico 1.16 in 0.0897 seconds.