The generator matrix

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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+240x^75+342x^76+648x^77+1278x^78+492x^79+648x^80+940x^81+504x^82+648x^83+678x^84+84x^85+18x^87+12x^88+2x^90+24x^94+2x^99

The gray image is a linear code over GF(3) with n=360, k=8 and d=225.
This code was found by Heurico 1.16 in 0.0829 seconds.