The generator matrix

 1  0  1  1  1  4  1  2  1  1  1 14  6  1  1  1  1 10  1  1 12  1  1  1  1  1  1  2  6  4 12  1 12  1
 0  1  1  0  3  1 15  1  6  5  2  1  1 15  9  8  9  1  5  6  1  4  5  0  7  7 12 10  1  2  8  2  1  0
 0  0  2  6  0  2  6  2  0  8  6 12  8  2 10  0  4 10  4  6  6  2 10 10  0  2  8  6 12  6  2  8  2  2
 0  0  0 12  0  0  8  8  0  0  4  0  0  4 12  4  4 12 12  0  8  0  4  4  4  8  8  0  4 12  4  4  8 12
 0  0  0  0  8  0  0  0  0  8  0  0  0  0  0  0  8  0  8  0  8  8  8  8  0  8  8  8  8  8  0  8  8  8
 0  0  0  0  0  8  8  0  8  8  8  8  0  8  0  0  8  8  0  8  0  0  0  8  8  8  8  0  0  8  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+188x^28+396x^29+1006x^30+2412x^31+3411x^32+5912x^33+6102x^34+5912x^35+3616x^36+2364x^37+794x^38+380x^39+188x^40+32x^41+34x^42+20x^44

The gray image is a code over GF(2) with n=272, k=15 and d=112.
This code was found by Heurico 1.16 in 12 seconds.