The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+86x^28+36x^29+162x^30+300x^31+1332x^32+1636x^33+3274x^34+2732x^35+3358x^36+1612x^37+1254x^38+292x^39+176x^40+44x^41+46x^42+4x^43+28x^44+11x^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 1.59 seconds.