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

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

Homogenous weight enumerator: w(x)=1x^0+54x^30+74x^31+164x^32+196x^33+320x^34+374x^35+856x^36+1850x^37+2711x^38+3206x^39+2712x^40+1874x^41+856x^42+366x^43+306x^44+158x^45+130x^46+72x^47+51x^48+18x^49+22x^50+4x^51+6x^52+1x^54+2x^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 3.59 seconds.