The generator matrix

 1  0  0  1  1  1 21  1  1  1  1 21  1  1
 0  1  0  7  3  1  1 15 26 20  0  1 17 14
 0  0  1 14  2  1 14 16 24 14 26 18 16  7
 0  0  0  9 18  0 18 18  9 18  9  9  0 18

generates a code of length 14 over Z27 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+348x^22+198x^23+2218x^24+1950x^25+6534x^26+8154x^27+15498x^28+12906x^29+8224x^30+2586x^31+288x^32+104x^33+30x^34+8x^36+2x^39

The gray image is a code over GF(3) with n=126, k=10 and d=66.
This code was found by Heurico 1.16 in 1.04 seconds.