The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  0  2  4  2  2  8  2  8  1  1  1  1  1
 0  2  0  2  0 10 12 14  4  4  6  6 10  2  0  8  2  6 14  2  4  4 12 12 10 14 10
 0  0  2  2 12 14  6  4  4  2  6  0  6  0  2  2  2  0  4  4  2  2  8  8  0  4  0
 0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  8  8  0  0  8  8  0
 0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  8  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  8  0  0  0  8  8  8  8  0  8
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  0  8  8  0  8  8  0  8  8  0  0  0  0
 0  0  0  0  0  0  0  8  8  8  0  0  8  0  8  0  8  0  0  8  8  0  0  8  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+95x^20+158x^21+442x^22+874x^23+2234x^24+3366x^25+5938x^26+6514x^27+5944x^28+3482x^29+2230x^30+798x^31+417x^32+162x^33+86x^34+6x^35+9x^36+8x^38+4x^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 5.13 seconds.