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

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

Homogenous weight enumerator: w(x)=1x^0+196x^28+512x^30+32x^31+1142x^32+320x^33+2146x^34+3040x^35+6204x^36+5504x^37+6200x^38+3040x^39+2378x^40+320x^41+1004x^42+32x^43+522x^44+120x^46+47x^48+2x^50+5x^52+1x^68

The gray image is a code over GF(2) with n=296, k=15 and d=112.
This code was found by Heurico 1.16 in 12.5 seconds.