The generator matrix

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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+222x^77+254x^78+1002x^79+990x^80+442x^81+954x^82+624x^83+430x^84+936x^85+582x^86+50x^87+18x^88+10x^90+6x^92+14x^93+6x^95+14x^96+6x^97

The gray image is a linear code over GF(3) with n=369, k=8 and d=231.
This code was found by Heurico 1.16 in 0.0865 seconds.