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

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

Homogenous weight enumerator: w(x)=1x^0+310x^78+324x^80+414x^81+648x^83+354x^84+64x^87+42x^90+24x^93+4x^96+2x^108

The gray image is a code over GF(3) with n=369, k=7 and d=234.
This code was found by Heurico 1.16 in 20.4 seconds.