The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^31+275x^32+896x^33+2544x^34+4078x^35+7814x^36+10548x^37+12948x^38+10696x^39+8194x^40+4140x^41+2108x^42+720x^43+354x^44+92x^45+60x^46+14x^47+2x^48+4x^49+4x^50+2x^51

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 19.4 seconds.