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

generates a code of length 40 over Z27 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+12x^78+210x^80+8x^81+4x^84+6x^89+2x^93

The gray image is a code over GF(3) with n=360, k=5 and d=234.
This code was found by Heurico 1.16 in 0.014 seconds.