The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+63x^28+138x^29+391x^30+560x^31+1116x^32+1802x^33+2260x^34+3722x^35+2311x^36+1810x^37+1117x^38+542x^39+327x^40+86x^41+63x^42+38x^43+22x^44+4x^45+8x^46+2x^47+1x^50

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 2.14 seconds.