The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+227x^20+56x^21+584x^22+656x^23+2314x^24+3016x^25+6014x^26+6880x^27+6252x^28+3016x^29+2222x^30+656x^31+634x^32+56x^33+138x^34+41x^36+2x^38+2x^40+1x^48

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 13.3 seconds.