The generator matrix

 1  0  0  1  1  1 15  1  1  3  1  1 12 24
 0  1  0  1 15 26  1 19 20  1 18  8  0  1
 0  0  1 26 16 26 22 19 21 23 20 20  1 22
 0  0  0 24 15  9  3 21  3 12  6 24  6  0

generates a code of length 14 over Z27 who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+122x^21+1104x^22+990x^23+5562x^24+5028x^25+23130x^26+21642x^27+44064x^28+44766x^29+21754x^30+7068x^31+1548x^32+240x^33+84x^34+36x^35+8x^36

The gray image is a code over GF(3) with n=126, k=11 and d=63.
This code was found by Heurico 1.16 in 8.94 seconds.