The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+60x^27+324x^28+700x^29+1328x^30+2244x^31+3659x^32+5064x^33+5675x^34+5424x^35+3881x^36+2222x^37+1200x^38+556x^39+254x^40+92x^41+51x^42+20x^43+9x^44+2x^45+2x^46

The gray image is a code over GF(2) with n=272, k=15 and d=108.
This code was found by Heurico 1.16 in 7.84 seconds.