The generator matrix

 1  0  0  0  1  1  1 24  1  1  1  1  1  1
 0  1  0  0 15 19 16  1 18  7  1 24  3 25
 0  0  1  0 16 19 14 25 24  2  3 15 17 14
 0  0  0  1 14 21 17  2  4  1 24  8 23 14

generates a code of length 14 over Z27 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+228x^20+220x^21+3402x^22+2838x^23+14644x^24+17532x^25+73086x^26+57362x^27+133704x^28+141216x^29+57138x^30+24084x^31+5190x^32+632x^33+126x^34+30x^35+6x^36+2x^39

The gray image is a code over GF(3) with n=126, k=12 and d=60.
This code was found by Heurico 1.16 in 66.5 seconds.