The generator matrix

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

generates a code of length 41 over Z3[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+18x^78+558x^79+180x^80+26x^81+684x^82+72x^83+18x^84+522x^85+72x^86+12x^87+18x^88+6x^96

The gray image is a linear code over GF(3) with n=369, k=7 and d=234.
This code was found by Heurico 1.16 in 0.0242 seconds.