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  1  3  1  1  1  1
 0  9  0  0  9  0  9  9 18  0  0  9  9  0 18  9 18 18  0  9 18  0  9 18 18 18 18  0  0  0  9  9  0  9  9 18  9  0  0  9  9
 0  0  9  0 18  9 18  9 18  0  9  9  0 18  0  0  9  9 18 18 18 18  9  0  0  9 18  0  0  9 18  9  9 18  0 18  0  0  9  9 18
 0  0  0  9 18 18  0 18 18 18  9  0 18  0 18  9  9  0  9  9  9 18  9  0  9 18  0  0  9 18 18 18  9  9  9 18 18 18  0  0  9

generates a code of length 41 over Z27 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+30x^78+54x^80+20x^81+486x^82+108x^83+12x^84+6x^87+6x^90+4x^93+2x^120

The gray image is a code over GF(3) with n=369, k=6 and d=234.
This code was found by Heurico 1.16 in 0.0182 seconds.