The generator matrix

 1  0  1  1  1  1 18  1  1  1  1 24  1  0
 0  1  1 26  7 18  1 25 20  1  3  1  0  1
 0  0 24  0  0 21 21  3  9 12 21  9  6  0
 0  0  0  9  0  9 18  0  9 18  0 18  9  0
 0  0  0  0  9  0 18  9  9  9  0  0  9 18

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

Homogenous weight enumerator: w(x)=1x^0+66x^20+90x^21+210x^22+348x^23+1922x^24+942x^25+8550x^26+7288x^27+13572x^28+16638x^29+7268x^30+1266x^31+588x^32+166x^33+48x^34+54x^35+28x^36+4x^39

The gray image is a code over GF(3) with n=126, k=10 and d=60.
This code was found by Heurico 1.16 in 28.8 seconds.