The generator matrix

 1  0  1  1  1 12  1  1  2  1 14  1 10  1 12  1  1  1  1  1  1  1 10 12  0  1  1  4  1  1  2  8  1  4 12  1  1  1
 0  1  1 12 11  1  2  7  1 14  1 13  1  0  1  3  5 11  4  4  5  3  1  2  1  1  6  1  4  7 14  4  4  1  1 10  3  2
 0  0  2  6  4  6  2 14  2  4  4  4  6 14  8  0  0  2  2  4  6  6  8  6 14  4  0 10  4  2  2  2  2  2 10 14  0  2
 0  0  0  8  0  0  0  0  0  0  8  8  0  8  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  8  0  8  0  0  0  8  0  8
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  0  8  8  0  0  0  8  0  8  8  0  8  0  8  0  8  0  8  0  0  8  8  0  8
 0  0  0  0  0  8  0  0  8  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  0  0  8  0  0  0  0  8  8  8  8  8  0  8
 0  0  0  0  0  0  8  0  0  0  8  8  8  0  0  8  0  8  0  8  0  8  8  8  8  8  0  0  0  0  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  8  8  0  8  0  0  0  0  8  8  0  0  8  0  8  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+53x^30+170x^31+468x^32+812x^33+2337x^34+4430x^35+6822x^36+12498x^37+10250x^38+12530x^39+7093x^40+4442x^41+2144x^42+778x^43+430x^44+166x^45+55x^46+12x^47+29x^48+2x^49+7x^50+4x^52+2x^54+1x^56

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 23 seconds.