The generator matrix

 1  0  1  1  1 12  1  1  2 14  1  1  1  1  6  4  0  1  1  8  8  1 10  1  2  2  2
 0  1  1 12 11  1  2  7  1  1 13  8  6  3  1  1  0 14  9  1  1 10  1  5  4 14  6
 0  0  2  6  4  6  2 14  2  4  4  2  0  0  0  2  2  4  6  4  4  8  6  0  2 12  8
 0  0  0  8  0  0  0  0  0  8  8  0  8  0  0  0  8  8  8  8  0  0  0  8  8  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  8  0  8  0  8  0  8
 0  0  0  0  0  8  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  0  8  8
 0  0  0  0  0  0  8  0  0  8  8  8  8  0  8  8  0  0  0  8  8  8  0  8  8  8  8
 0  0  0  0  0  0  0  8  8  0  0  8  8  8  0  0  8  8  0  0  8  0  8  0  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+135x^20+132x^21+652x^22+1452x^23+3927x^24+7044x^25+11620x^26+15532x^27+11778x^28+7020x^29+3892x^30+1444x^31+629x^32+140x^33+92x^34+4x^35+39x^36+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 13 seconds.