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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+216x^76+72x^77+262x^78+438x^79+372x^80+246x^81+438x^82+18x^83+30x^84+6x^85+18x^86+26x^87+12x^88+6x^89+12x^91+12x^94+2x^108

The gray image is a linear code over GF(3) with n=360, k=7 and d=228.
This code was found by Heurico 1.16 in 1.35 seconds.