The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  4 12  1  1  1  1  2  1  1  1  6  8  1  1  1  6  1  4 10  1  1  1  4 10 12  2  1
 0  1  1  0  3  1  5  4  1  8  3  1  1 10  3  2  4  1  9  7  5  1  1  2 12 15  1  9  2  1 15  8  9  2  1  8  4 11
 0  0  2  0  0  0  2 10  6  2  8 14  4 12  2  8  6 12 14  0  0 12 10 14 12  4 14  6  2  0 10  8  8  0  4  4  6  4
 0  0  0  2  0  2  2  8 14 14  6  4  2 10  2  4 10  0  8 12 14  4 14  4 12 12  0 12  6 14  4 12  8 14  2  2  4  8
 0  0  0  0  8  0  0  8  8  8  8  8  0  0  0  0  8  0  0  8  0  8  0  0  8  0  8  0  8  8  8  8  0  0  8  8  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  8  8  0  0  8  0  0  0  0  8  0  8  0

generates a code of length 38 over Z16 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+136x^31+456x^32+1234x^33+2109x^34+4810x^35+6998x^36+11360x^37+11014x^38+11812x^39+7160x^40+4630x^41+2050x^42+1138x^43+354x^44+180x^45+56x^46+24x^47+7x^48+4x^49+1x^50+2x^54

The gray image is a code over GF(2) with n=304, k=16 and d=124.
This code was found by Heurico 1.16 in 23.9 seconds.