The generator matrix

 1  0  1  1  1 12  6  1  1  1  1 10  1  1  0  4  1  1  2  1  1  1  2  1  1  1  1 14  2 12  0  0 10  8  1  1  1  1
 0  1  1  4  3  1  1  6 13  2  7  1 12 11  1  1  1  4  1 10 15 12  1  5  5 13  9  1  4  0  2  1  1  4 14  0  4  4
 0  0  2  2  0  6  0  8  4  2  2  6  6 10 14  4  4 12  2  6  8  8  4  0  8 10  6  4  2  2  6  8 10  2 12  8 12  2
 0  0  0  8  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  8  8  0  0  8  8  8  8  0  8  0  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  0  8  0  8  0  8  8  8  0  8  8  0  0  8  8  0  0  8  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  0  0  8  8  8  0  0  8  8  8  8  0  8  8  0  0  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  8  8  0  0  0  0  8  8  8  8  0  8  0  8  0  0  0  0  0  8  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+62x^31+188x^32+578x^33+1073x^34+2396x^35+3782x^36+5384x^37+5836x^38+5496x^39+3790x^40+2396x^41+970x^42+468x^43+168x^44+88x^45+52x^46+26x^47+5x^48+2x^49+5x^50+2x^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 6.32 seconds.