The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+81x^28+446x^29+722x^30+1190x^31+1852x^32+2548x^33+2685x^34+2654x^35+1839x^36+1246x^37+591x^38+308x^39+143x^40+48x^41+11x^42+6x^43+4x^44+7x^46+2x^47

The gray image is a code over GF(2) with n=272, k=14 and d=112.
This code was found by Heurico 1.16 in 2.11 seconds.