The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+33x^26+12x^27+84x^28+40x^29+117x^30+256x^31+133x^32+1240x^33+156x^34+4072x^35+160x^36+1240x^37+124x^38+256x^39+88x^40+40x^41+65x^42+12x^43+44x^44+13x^46+2x^48+2x^50+2x^54

The gray image is a code over GF(2) with n=280, k=13 and d=104.
This code was found by Heurico 1.16 in 0.816 seconds.