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

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+74x^75+168x^76+108x^77+122x^78+468x^79+486x^80+118x^81+468x^82+44x^84+12x^85+54x^86+34x^87+18x^88+8x^90+2x^93+2x^108

The gray image is a linear code over GF(3) with n=360, k=7 and d=225.
This code was found by Heurico 1.16 in 0.0366 seconds.