The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1  1 12 10  1  1  1  1  1  0  1  6  1  1  1  1  0  0  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6 12 10  1  1  5 15  9  0  6  1  3  1  5 15  0  6  1  1  3  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  8  8  8  0  0  0  0  0  0  0  8  0  8  8  8  0  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  0  8  0  8  8  0  8  0  8  0  8  0  0  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  8  8  8  8  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  0  8  8  8  0  8  0  0  8  8  0  0  8  0  0  8  0  8  0  8  8
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  8  8  8  8  8  0  8  8  8  0  8  8  8  0  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  0  8  0  8  0  0  8  0  8  8  8  0  8  0  0  0  0  8
 0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  8  0  0  0  0  8  8  0  8  8  0  0  0  0  0  0  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+112x^28+36x^30+32x^31+597x^32+480x^33+1584x^34+3488x^35+10047x^36+8288x^37+16216x^38+8288x^39+10051x^40+3488x^41+1584x^42+480x^43+579x^44+32x^45+36x^46+101x^48+13x^52+1x^56+1x^60+1x^64

The gray image is a code over GF(2) with n=304, k=16 and d=112.
This code was found by Heurico 1.16 in 21.5 seconds.