The generator matrix

 1  0  1  1  1  6  1  1  0  1 14  1  1  1 14  1  8  1  1  1  1  4  2  1  1 12  1  1  1  8  1  0  1  1  0  1  1  1
 0  1 11  6  1  1  8  5  1 10  1  3  5  8  1  6  1 13  5  6  4  1  1 13  7  1 12  0  1  1  9  1  0 12  1 11 12  8
 0  0 12  0  0  0  0  0  0  0  0  4  4  4  4 12 12  4  8  4 12  4 12  8 12  8 12 12 12 12 12  4  4  8  0 12  4  8
 0  0  0 12  0  0  0  0  4 12 12  8  4  8  0 12 12 12 12  8  4 12  0  4  0  8  8 12  4  0  4  8  0  4  8 12  8  4
 0  0  0  0  4  0  8  4  0  8  0  8  8 12  4 12 12  0  4  4  4 12  4  4  8  0 12  8 12  0 12  0  0 12 12 12  0  8
 0  0  0  0  0 12 12  4 12  4  8  4  0 12 12 12  8 12  8  8  8  0 12 12  8  0  8  8  0  0 12 12  0  0  4  8 12  8

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

Homogenous weight enumerator: w(x)=1x^0+150x^30+36x^31+612x^32+684x^33+1714x^34+3876x^35+6907x^36+12812x^37+11990x^38+12812x^39+6930x^40+3876x^41+1680x^42+684x^43+515x^44+36x^45+168x^46+40x^48+10x^50+2x^52+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 26 seconds.