The generator matrix

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

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+486x^75+1590x^76+1638x^77+4762x^78+6132x^79+8028x^80+13946x^81+16074x^82+19476x^83+24030x^84+22686x^85+20394x^86+18604x^87+10308x^88+4338x^89+2856x^90+1260x^91+72x^92+144x^93+240x^94+52x^96+30x^97

The gray image is a linear code over GF(3) with n=378, k=11 and d=225.
This code was found by Heurico 1.16 in 67.5 seconds.