The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+72x^27+317x^28+704x^29+1181x^30+2168x^31+3583x^32+5178x^33+6222x^34+5402x^35+3646x^36+2142x^37+1120x^38+598x^39+248x^40+102x^41+50x^42+14x^43+13x^44+2x^45+3x^46+2x^47

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 7.49 seconds.