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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+420x^75+1056x^78+324x^80+1190x^81+2430x^82+1296x^83+4228x^84+4860x^85+1296x^86+1250x^87+808x^90+406x^93+104x^96+6x^99+4x^102+2x^105+2x^117

The gray image is a linear code over GF(3) with n=378, k=9 and d=225.
This code was found by Heurico 1.16 in 2.41 seconds.