The generator matrix

 1  0  0  0  1  1  1  1  1  6  1 15  1
 0  1  0  0 18 19 21 25 23  1 17  1  6
 0  0  1  0 16 19  7 23  2  8  6 23  9
 0  0  0  1 14 21 25  2  1  1 11  8  7

generates a code of length 13 over Z27 who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+144x^19+3162x^20+2664x^21+14040x^22+15828x^23+71886x^24+55350x^25+145602x^26+140816x^27+55584x^28+21912x^29+4050x^30+270x^31+120x^32+6x^33+6x^36

The gray image is a code over GF(3) with n=117, k=12 and d=57.
This code was found by Heurico 1.16 in 72.1 seconds.