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

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+238x^75+204x^76+210x^77+636x^78+216x^79+828x^80+990x^81+1722x^82+2208x^83+4334x^84+3168x^85+2220x^86+1022x^87+312x^88+186x^89+494x^90+132x^91+132x^92+234x^93+66x^94+36x^95+68x^96+12x^97+12x^98+2x^114

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 1.16 seconds.