The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  8  2  1  0  1  1  2  1  1  1  1  1  2  4  1  1
 0  2  0 14  4  6 12  2  0  6  6  2 14 12  2 14 10 10  8  6  8 14  6 14  4  0  0
 0  0 12  4  4  0  0  4  0  8  0  4  4  8  0  4  0  8  4  8  4 12 12 12  4  0  0
 0  0  0  8  0  0  0  8  0  0  0  0  8  8  8  0  8  8  8  0  8  8  0  0  0  8  0
 0  0  0  0  8  0  0  8  8  8  8  0  8  0  8  0  8  0  0  0  8  0  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  8  8  8  0  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  8  8  0  8  8  0  8  0  8  8  0  8  0  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+15x^20+62x^21+134x^22+168x^23+511x^24+850x^25+1393x^26+1948x^27+1402x^28+834x^29+496x^30+176x^31+109x^32+46x^33+22x^34+12x^35+7x^36+2x^38+3x^40+1x^42

The gray image is a code over GF(2) with n=216, k=13 and d=80.
This code was found by Heurico 1.16 in 0.381 seconds.