The generator matrix

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

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+356x^78+414x^79+2004x^80+1802x^81+1884x^82+2826x^83+2134x^84+1734x^85+2412x^86+1396x^87+942x^88+1164x^89+504x^90+48x^91+6x^92+38x^93+6x^95+6x^96+6x^98

The gray image is a linear code over GF(3) with n=378, k=9 and d=234.
This code was found by Heurico 1.16 in 0.514 seconds.