The generator matrix

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

generates a code of length 37 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+46x^28+62x^29+186x^30+182x^31+298x^32+430x^33+985x^34+1758x^35+2580x^36+3364x^37+2588x^38+1742x^39+1014x^40+408x^41+267x^42+146x^43+142x^44+86x^45+66x^46+12x^47+15x^48+2x^49+3x^50+1x^58

The gray image is a code over GF(2) with n=296, k=14 and d=112.
This code was found by Heurico 1.16 in 3.22 seconds.