The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+73x^30+468x^31+737x^32+1676x^33+2441x^34+5070x^35+7048x^36+10132x^37+10188x^38+10298x^39+6930x^40+5088x^41+2547x^42+1650x^43+630x^44+372x^45+105x^46+50x^47+12x^48+12x^49+3x^50+2x^52+2x^54+1x^58

The gray image is a code over GF(2) with n=304, k=16 and d=120.
This code was found by Heurico 1.16 in 33.3 seconds.