The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+281x^20+208x^21+1122x^22+1136x^23+3649x^24+7008x^25+11200x^26+15920x^27+11484x^28+7312x^29+3776x^30+976x^31+987x^32+192x^33+216x^34+16x^35+43x^36+6x^38+3x^40

The gray image is a code over GF(2) with n=216, k=16 and d=80.
This code was found by Heurico 1.16 in 28 seconds.