The generator matrix

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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+900x^77+1518x^78+1836x^79+4218x^80+4618x^81+4158x^82+8412x^83+7224x^84+5778x^85+8466x^86+5034x^87+2646x^88+2628x^89+1220x^90+162x^91+102x^92+66x^93+48x^95+12x^98+2x^99

The gray image is a linear code over GF(3) with n=378, k=10 and d=231.
This code was found by Heurico 1.16 in 75.2 seconds.