The generator matrix

 1  0  1  1  1 12  1  1 10  1  1  6  1  2  8 14  1  1  1  4  1  2  1  1  1  2  1
 0  1  1 12 11  1  2  7  1  6  5  1 11  1  1  1  4  9  7  1  5  1 10 12  3  8  0
 0  0  2  6  4  6  2  2  6  0  0  8  2  2  4  2 10  6  4  4  6 12  8  0  8 12  0
 0  0  0  8  0  0  0  8  8  8  8  8  0  0  0  0  0  0  8  8  0  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  8  0  8  8  0  8  8  8  8  8  0  0  8  8  8  0  8  0
 0  0  0  0  0  8  0  0  8  0  0  0  0  8  0  8  0  8  8  8  8  8  8  0  0  0  0
 0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  0  8  0  8  0  0  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+43x^20+134x^21+227x^22+566x^23+1893x^24+3834x^25+6306x^26+6802x^27+6276x^28+3850x^29+1876x^30+554x^31+215x^32+118x^33+38x^34+14x^35+17x^36+1x^38+3x^40

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 3.45 seconds.