The generator matrix

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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+228x^80+214x^81+162x^82+342x^83+350x^84+324x^85+318x^86+120x^87+42x^89+22x^90+18x^92+20x^93+24x^95+2x^111

The gray image is a linear code over GF(3) with n=378, k=7 and d=240.
This code was found by Heurico 1.16 in 0.278 seconds.