The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^28+78x^29+172x^30+182x^31+307x^32+234x^33+877x^34+332x^35+3619x^36+4468x^37+3942x^38+336x^39+724x^40+292x^41+331x^42+164x^43+133x^44+46x^45+44x^46+10x^47+24x^48+2x^49+7x^50+1x^52+2x^54+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.