The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+42x^29+155x^30+416x^31+733x^32+1330x^33+2878x^34+4676x^35+7185x^36+9842x^37+10697x^38+10014x^39+7571x^40+4756x^41+2683x^42+1274x^43+665x^44+330x^45+160x^46+66x^47+35x^48+18x^49+3x^50+2x^51+2x^52+2x^53

The gray image is a code over GF(2) with n=304, k=16 and d=116.
This code was found by Heurico 1.16 in 35.5 seconds.