The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  1  1  4  1  4  2  1  2  1  2  2  2  4  1  0  1  2  1  1
 0 12  0  4  0  0  4 12  0  0  4 12  8  4 12 12  0  4  0  0 12  4 12 12  8  4 12  4  8  4  8 12 12  0  0
 0  0 12  4  0 12  4  0  0 12  4  0  4 12  8  0  0  4 12 12  8 12  0  8  0  4  8 12  4  8  4  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  0  8  0  8  0  0  0  8  8  8  0  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  8  8  8  0  8  8  8  8  0  0  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  0  8  8  0  8  8  0  0  8  8  8  0  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  8  8  8  0  8  8  8  8  0  8  8  8  0  8  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  8  8  0  8  8  0  0  8  0  0  0  8  8  8  0  8  0  0  8  8  8  0  0
 0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  8  0  0  8  8  8  8  0  8  8  0  0  8  0  8  0  8  8  8  8
 0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  8  0  8  8  0  8  0  8  8  0  8  0  8  0  8

generates a code of length 35 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+57x^24+216x^26+480x^28+32x^29+985x^30+320x^31+2285x^32+3040x^33+6145x^34+5504x^35+6274x^36+3040x^37+2386x^38+320x^39+942x^40+32x^41+450x^42+172x^44+53x^46+26x^48+5x^50+2x^52+1x^56

The gray image is a code over GF(2) with n=280, k=15 and d=96.
This code was found by Heurico 1.16 in 9.76 seconds.