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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+88x^78+216x^79+744x^80+400x^81+324x^82+1110x^83+694x^84+648x^85+1242x^86+474x^87+270x^88+282x^89+28x^90+24x^92+10x^93+4x^102+2x^114

The gray image is a linear code over GF(3) with n=378, k=8 and d=234.
This code was found by Heurico 1.16 in 0.0939 seconds.