The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^30+172x^31+311x^32+942x^33+1104x^34+2770x^35+4623x^36+7236x^37+9347x^38+11912x^39+9291x^40+8408x^41+4383x^42+2528x^43+1193x^44+640x^45+317x^46+148x^47+65x^48+50x^49+21x^50+6x^51+4x^52+4x^53

The gray image is a code over GF(2) with n=312, k=16 and d=120.
This code was found by Heurico 1.16 in 36.8 seconds.