The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+168x^28+58x^30+544x^32+64x^33+658x^34+384x^35+3007x^36+3008x^37+5668x^38+5376x^39+6157x^40+3008x^41+2596x^42+384x^43+1061x^44+64x^45+226x^46+263x^48+10x^50+49x^52+11x^56+3x^60

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 16.6 seconds.