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  3  1  1  1  1  3  3  1  3
 0  3  0  9 24 21  3 15 24  9  9 15 18 12 15 21 24 21 18 12  9 24 12  6 15 21 18 12  9 12  0  3  0 24 21 21 24  0 18 15
 0  0  3 15  9  6  3 21 15  0  6 18 21 24 12 12 24  0 24  3  9 21 18  6  0 24  9  9  3  6 21 12 18  3 18 21  6 24 12 21

generates a code of length 40 over Z27 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+264x^76+242x^78+510x^79+324x^80+268x^81+444x^82+48x^84+12x^85+4x^87+48x^88+2x^90+6x^91+12x^94+2x^108

The gray image is a code over GF(3) with n=360, k=7 and d=228.
This code was found by Heurico 1.16 in 0.0469 seconds.