The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  2  0  1  2  1  1  1 12  1  1  2  1  0  2  1 12  1  1  1  2  1  1  2  1  4  0  1  1
 0  2 12  6  0  6 12 10  0  6 12  6  2 10 10  6  0 12  2 10 10  6  0  2 10  6  2  6 12  0  6 10  6  6  0  0  2  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  8  8  8  0  8  8  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  0  0  8  0  8  8  8  0  0  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  0  0  0  8  8  0  0  0  0  0  0  0  0  8  8  0  8  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  0  0  8  0  0  0  0  8  8  8  0  8  8  8  8  0  0  0  0  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  8  0  8  8  0  8  8  8  8  0  8  8  8  0  0  8  0  0  0  0  0  0  8  8  0
 0  0  0  0  0  0  0  8  0  0  0  8  8  0  8  0  0  0  8  0  0  8  0  8  8  0  8  0  8  8  8  8  8  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  0  8  8  0  8  8  0  0  0  8  0  0  8  0  8  8  8  0  8  8  0  0  0
 0  0  0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  0  8  8  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  8  0  0

generates a code of length 39 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+65x^28+8x^29+51x^30+84x^31+218x^32+380x^33+372x^34+1360x^35+1462x^36+5232x^37+3016x^38+8376x^39+2866x^40+5272x^41+1440x^42+1360x^43+453x^44+360x^45+168x^46+84x^47+51x^48+12x^49+60x^50+4x^52+12x^54+1x^62

The gray image is a code over GF(2) with n=312, k=15 and d=112.
This code was found by Heurico 1.16 in 9.54 seconds.