The generator matrix
1 0 0 1 1 1 15 1 1 1 24 15 1
0 1 0 1 15 26 1 16 17 18 24 1 0
0 0 1 26 16 26 22 20 18 21 1 11 1
0 0 0 24 15 9 3 3 21 6 6 18 12
generates a code of length 13 over Z27 who´s minimum homogenous weight is 19.
Homogenous weight enumerator: w(x)=1x^0+126x^19+984x^20+792x^21+4716x^22+5244x^23+24204x^24+17658x^25+49320x^26+47396x^27+18072x^28+7080x^29+1224x^30+252x^31+66x^32+6x^33+6x^36
The gray image is a code over GF(3) with n=117, k=11 and d=57.
This code was found by Heurico 1.16 in 7.69 seconds.