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  1  1  2  2  4  1  2  2  1
 0 12  0  0  0  0  0  0  0  0  8 12 12  4  8 12  4 12  0  8  4  0  8  0 12 12  8 12  0  4  8  4  8  0  8 12  0
 0  0 12  0  0  0  0  0  0  0 12 12  4  8  4  4  0  8  4 12  4  8  0 12 12  4  8  0 12  8  0 12 12 12 12  4  0
 0  0  0 12  0  0  8 12 12  4  4  8  4  4 12  8 12  8  4  8  4  0 12  0 12  0  0  4  8  0  0  0  0  4  4  0  0
 0  0  0  0 12  0 12 12  4  8  0  0  0  0  8  4  4  4  4  0 12 12  0  8  4  8  4  8  0  8  4  4  0  4  0 12  0
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  4  8  4 12  0 12  8  0  8  8 12  0  4 12 12 12  0 12 12  4  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+44x^28+68x^29+176x^30+214x^31+220x^32+354x^33+522x^34+792x^35+3148x^36+5304x^37+3124x^38+850x^39+530x^40+364x^41+210x^42+174x^43+144x^44+52x^45+59x^46+16x^47+9x^48+2x^49+4x^50+2x^51+1x^62

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 3.25 seconds.