The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  2  1  1  1  1 12  1  1  2  0  2  1 12  2  1  0 12  1  1  2  2  2  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  6  2 10  0  6 12 10  2 12  6  6  2 10 10  2  6  0  2  2  0 12  6  6  0  0  6
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  8  0  8  8  0  8  8  0  8  8  8  0  0  8  8  0  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  8  8  8  8  8  8  8  8  8  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  8  0  0  0  0  8  0  8  0  8  0  0  0  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  8  8  8  0  8  0  8  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  0  8  8  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  8  0  0  0  0  8  8  0  8  8  8  0  8  8  0  8  0  8  0  0  8  0  0  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  8  8  8  0  8  0  0  8  0  8  8  8  0  8  8  8  8  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  8  0  0  8  8  8  8  8  8  8  0  0  8  0  0  0  8  8  8  8  8  8

generates a code of length 38 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+105x^28+86x^30+32x^31+590x^32+416x^33+1040x^34+2656x^35+3167x^36+6112x^37+4396x^38+6112x^39+3127x^40+2656x^41+1056x^42+416x^43+569x^44+32x^45+78x^46+105x^48+13x^52+1x^56+2x^60

The gray image is a code over GF(2) with n=304, k=15 and d=112.
This code was found by Heurico 1.16 in 9.57 seconds.