The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  0  2  1  2  1  1 12  2  1  1  4  2  1  2  4  2  4  4  2  2  1  1
 0  2  0 14  4  6 12  2  0  6 14 12  6  2  8  2  2 14  4 10  0 14  2  2 10 14  2  8 12  6  4 10  8  8  0  8  0  0
 0  0 12  4  4  0  0  4  0  0  4  8  0  4  4  4  0  4  4  8  0  4  8 12  8  4 12  4  0  0 12  8  4  4 12 12  0  0
 0  0  0  8  0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  0  8  8  0  8  0  0  8  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  0  8  8  0  8  8  8  8  0  8  8  8  8  8  0  0  8  8  0  0  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  8  8  8  0  8  0  8  8  8  0  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  8  0  8  0  0  0  0  8  8  8  8  8  8  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  8  0  8  0  8  0  0  0  8  8  8  8  8  0  0  8  0  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  0  0  8  8  0  8  0  8  8  0  0  8  8  8  0  0  0  0  8  8  8

generates a code of length 38 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+112x^28+204x^30+56x^31+791x^32+520x^33+1608x^34+1944x^35+4458x^36+3624x^37+6128x^38+3624x^39+4510x^40+1944x^41+1576x^42+520x^43+772x^44+56x^45+196x^46+88x^48+16x^50+18x^52+2x^56

The gray image is a code over GF(2) with n=304, k=15 and d=112.
This code was found by Heurico 1.16 in 9.53 seconds.