The generator matrix

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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+103x^30+4x^31+364x^32+136x^33+751x^34+1128x^35+2114x^36+4456x^37+3842x^38+6960x^39+3805x^40+4504x^41+2166x^42+1112x^43+788x^44+120x^45+275x^46+12x^47+83x^48+27x^50+10x^52+4x^54+3x^56

The gray image is a code over GF(2) with n=312, k=15 and d=120.
This code was found by Heurico 1.16 in 10.8 seconds.