The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2
 0 12  0  0  0  0  0  0  0  0  8 12 12  4  0  0  8  8 12  4  4  8 12  4 12  8  0
 0  0 12  0  0  0  0  0  0  0 12 12  4  8  8  4  0  8  4  0  4 12  8  4  4 12  4
 0  0  0 12  0  0  8 12 12  4  4  8  4  4  8  0  4  0  4  4  8 12  4 12  8 12  8
 0  0  0  0 12  0 12 12  4  8  0  0  0  0  0  8  8 12  8  4  0  4  4  0  8  4  4
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  8 12  8  0  0  8  4 12  4  4  4  0  8

generates a code of length 27 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+203x^20+412x^22+678x^24+1768x^26+10240x^27+1786x^28+668x^30+457x^32+160x^34+10x^36+1x^52

The gray image is a code over GF(2) with n=216, k=14 and d=80.
This code was found by Heurico 1.16 in 2.54 seconds.