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

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

Homogenous weight enumerator: w(x)=1x^0+116x^28+214x^30+40x^31+584x^32+184x^33+1374x^34+968x^35+2842x^36+3736x^37+2752x^38+1016x^39+1551x^40+168x^41+464x^42+24x^43+236x^44+8x^45+58x^46+39x^48+2x^50+6x^52+1x^56

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 3.27 seconds.