The generator matrix

 1  0  1  1  1  4  1 10  1  1 14  1 12  1  1  1  1  2  2  1  1  1  1  8  0  2  1  1  1  1  1  1  1  1  4  6  1  1
 0  1  1  0 11  1 10  1  5  7  1  6  1 15  4  6 13  1  1 13  6  5  0  8  1  4 14  5 14  2  8  7  4 13  1  1  2  8
 0  0  2  6  4  6  2  2  8  2  4  0  2  6  2  4  0  0  2  6  2  4  6  2  4  2 10 14  0  8 10  4 12  0  0  4  2  0
 0  0  0 12  0  4  4 12  8  0  0  8  4  8  8  4  4 12  0  4 12  4  8 12  4  0  8 12 12  0  4  8  0  4 12  4  0  4
 0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  0  8  0  8  8  8  0  0  8  8  0  8  8  8  8  0  0  8  0  8  0  8  0
 0  0  0  0  0  8  8  0  8  8  8  8  8  8  0  8  8  8  0  8  8  0  8  0  8  8  0  0  8  0  0  8  8  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+34x^31+199x^32+482x^33+1127x^34+2174x^35+3959x^36+5442x^37+5829x^38+5694x^39+3962x^40+2068x^41+1115x^42+396x^43+152x^44+66x^45+23x^46+20x^47+14x^48+6x^49+2x^50+2x^51+1x^52

The gray image is a code over GF(2) with n=304, k=15 and d=124.
This code was found by Heurico 1.16 in 6.41 seconds.