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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+186x^79+270x^80+1062x^81+972x^82+408x^83+1086x^84+576x^85+294x^86+978x^87+516x^88+144x^89+14x^90+6x^92+12x^95+6x^96+18x^97+12x^99

The gray image is a linear code over GF(3) with n=378, k=8 and d=237.
This code was found by Heurico 1.16 in 0.09 seconds.