The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+42x^28+140x^29+371x^30+694x^31+1187x^32+1844x^33+2448x^34+2906x^35+2634x^36+1810x^37+1118x^38+596x^39+290x^40+168x^41+88x^42+26x^43+4x^44+6x^45+7x^46+2x^47+2x^48

The gray image is a code over GF(2) with n=280, k=14 and d=112.
This code was found by Heurico 1.16 in 2.24 seconds.