The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+47x^30+66x^31+204x^32+216x^33+295x^34+580x^35+1116x^36+1820x^37+2359x^38+2848x^39+2635x^40+1844x^41+983x^42+524x^43+320x^44+196x^45+137x^46+78x^47+71x^48+20x^49+17x^50+4x^52+1x^54+1x^56+1x^58

The gray image is a code over GF(2) with n=312, k=14 and d=120.
This code was found by Heurico 1.16 in 3.53 seconds.