The generator matrix

 1  0  0  1  1  1  6  1  1  1  1 10  6  1  0  1  1  4  2  4  1  1  1  0  4  6  1
 0  1  0  1  6  7  1  0 12 11  7  1  1  7  6  6  9  1  2  1 14  2  5  6  1  1  0
 0  0  1  1  3  2  3  6  3  7  4  5  0  1  1  5  6  1  1  7  1  2  6  1  1  3  0
 0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  8  8  0  8  8  0  8  0
 0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  8  0  8  8  8  0  0  0  0  8  8  0
 0  0  0  0  0  0  8  8  8  8  0  8  0  0  8  0  0  8  0  0  8  8  8  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+28x^20+154x^21+422x^22+1826x^23+3042x^24+8586x^25+9304x^26+18822x^27+9328x^28+8578x^29+3040x^30+1806x^31+387x^32+150x^33+32x^34+10x^35+12x^36+4x^37+2x^38+2x^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 10.5 seconds.