The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  0  2  0  2  1  1  1  2  1  1  1  1  8  1  2  1  1  1  4  2  2
 0  2  0  6  4  6 12  2  8  0  6  6  4  2  6  2 14 10 10  0  2 12  2 12 14  2  0  8 10 12  0  2  0  0
 0  0 12  0  4  0  0  0  8  4  4 12  8 12  0  8 12  0 12  0 12  4  4  8  4 12 12 12  8 12  4  8  0  4
 0  0  0 12  0  0  8 12 12 12 12  8  4 12  0  8  8  8 12  8  8  4  0 12 12  8  8  8  0 12  4  4  4  4
 0  0  0  0  8  0  8  8  0  0  8  0  8  8  8  0  0  8  0  8  8  8  0  8  8  0  8  8  0  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  0  0  8  8  8  8  0  8  0  8  0  8  8  8  0  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+111x^28+88x^29+374x^30+396x^31+749x^32+1828x^33+1160x^34+1832x^35+771x^36+368x^37+248x^38+76x^39+117x^40+20x^41+40x^42+10x^44+2x^46+1x^48

The gray image is a code over GF(2) with n=272, k=13 and d=112.
This code was found by Heurico 1.16 in 0.641 seconds.