The generator matrix

 1  0  0  1  1  1  1  1  9  1  1  1 15  1  1  1 12  1  3  1  1  1  1  0  1  1  1 18  1  6 12 24  1  1  1  1  1  1  1 21 21  1 15  3  1  1  1  3  1  6 24  1  1 24  1  1
 0  1  0 18  1 19 23 21  1  4  5 26  1  9 22  3  1 17  1 20 11  0 16 15 12 22 25  1 23  1  1 21  3 14 13 19 26  1  8  1  3 23  1  1 17 18 21  1 16  1  1  2  7  6 11  0
 0  0  1 16 25 18 17  8 22  5 22  6 20 21  7 23 13 11  0 12 10  4  2  1  0  1 15 26 11  3 20  1 16 12  8 19 14 15 18  7  1 10  7  8 26 23 21  3  8 15 18 26  9  1 13 15

generates a code of length 56 over Z27 who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+582x^106+1128x^107+1392x^108+2388x^109+2076x^110+1468x^111+2646x^112+1662x^113+1308x^114+1758x^115+1080x^116+584x^117+882x^118+516x^119+170x^120+12x^122+6x^123+6x^125+6x^126+6x^127+6x^129

The gray image is a code over GF(3) with n=504, k=9 and d=318.
This code was found by Heurico 1.16 in 0.726 seconds.