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

generates a code of length 42 over Z27 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+48x^78+192x^80+58x^81+372x^83+1030x^84+324x^86+30x^87+60x^89+16x^90+24x^92+24x^93+6x^96+2x^120

The gray image is a code over GF(3) with n=378, k=7 and d=234.
This code was found by Heurico 1.16 in 0.0408 seconds.