The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+72x^28+98x^30+290x^32+128x^33+1330x^34+256x^35+1375x^36+128x^37+214x^38+153x^40+22x^42+24x^44+3x^48+1x^52+1x^56

The gray image is a code over GF(2) with n=280, k=12 and d=112.
This code was found by Heurico 1.16 in 0.233 seconds.