The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+216x^20+80x^21+576x^22+584x^23+1887x^24+3080x^25+6456x^26+6864x^27+6702x^28+3040x^29+1814x^30+616x^31+607x^32+72x^33+110x^34+58x^36+2x^38+1x^40+2x^42

The gray image is a code over GF(2) with n=216, k=15 and d=80.
This code was found by Heurico 1.16 in 6.47 seconds.