The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^30+146x^31+276x^32+484x^33+1070x^34+2350x^35+3730x^36+5240x^37+6089x^38+5214x^39+3928x^40+2312x^41+934x^42+482x^43+232x^44+120x^45+60x^46+32x^47+23x^48+4x^49+2x^52+1x^54

The gray image is a code over GF(2) with n=304, k=15 and d=120.
This code was found by Heurico 1.16 in 6.7 seconds.