The generator matrix

 1  0  1  1  1  1  1 18  1  1  1  1  1
 0  1  1 26  0 25 17  1 18 25  4 15 18
 0  0 24  0  9  3 21  3 21 18 18 21 15
 0  0  0  3 15  9 15 15  9 21  6  6  3

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

Homogenous weight enumerator: w(x)=1x^0+114x^19+288x^20+380x^21+1584x^22+1014x^23+8324x^24+5472x^25+17640x^26+16240x^27+5718x^28+1350x^29+556x^30+234x^31+120x^32+10x^33+4x^36

The gray image is a code over GF(3) with n=117, k=10 and d=57.
This code was found by Heurico 1.16 in 1.11 seconds.