The generator matrix

 1  0  1  1  1  1  1  0  1  1 2X^2  1  1  1  1 2X  1  0  1  1 X^2+2X  1  1  1 X^2  1  1  X  1  1 X^2  1  1  1  1 X^2+X  1  X  1  1  X 2X^2+X
 0  1  1  2 2X^2 2X+1 2X^2+2  1  0 2X^2+X+1  1 2X^2+X+2  0  2 2X^2+X+1  1 2X+2  1 2X+1 2X^2  1 X^2+2X+2 2X X+1  1 2X^2+2X X^2+2X  1 2X^2+2X+1 2X+2  1 2X^2+2X+1 2X X^2+2X X^2+2  1 X^2+2X+2 2X^2+X 2X^2+2X+1  X X^2  1
 0  0 2X  0 2X^2  0 2X^2+X 2X 2X^2 2X^2+X X^2+X 2X X^2+2X  0  X X^2+X 2X^2+2X X^2+2X X^2+2X X^2+X 2X^2+X 2X^2 2X X^2 2X^2 2X 2X^2  X 2X^2+X 2X 2X 2X^2+2X X^2+X X^2+X X^2 X^2  X X^2 2X^2+2X X^2+2X  X  X
 0  0  0  X 2X^2+X X^2+X 2X^2 X^2 2X 2X X^2 2X 2X^2+2X 2X^2+2X  0 2X^2+X 2X^2 2X  X 2X^2 2X^2+2X 2X^2 X^2 2X 2X^2+X 2X^2+X  X  0 2X^2+2X  X 2X^2+X 2X X^2+2X X^2+X 2X^2  0 X^2  X 2X^2+X 2X 2X^2+2X  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+258x^75+318x^76+738x^77+1956x^78+1968x^79+2442x^80+5484x^81+4482x^82+5886x^83+9786x^84+6408x^85+5844x^86+7168x^87+2922x^88+1344x^89+1080x^90+342x^91+198x^92+204x^93+78x^94+60x^95+62x^96+6x^97+12x^98+2x^99

The gray image is a linear code over GF(3) with n=378, k=10 and d=225.
This code was found by Heurico 1.16 in 5.8 seconds.