The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^20+24x^21+264x^22+304x^23+1527x^24+1256x^25+3600x^26+1952x^27+4032x^28+1256x^29+1320x^30+304x^31+301x^32+24x^33+64x^34+38x^36+3x^40

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 1.65 seconds.