The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  2  0  1  2  1  1  1  1  1  1  1  2  8  2  1  1  0  1
 0  2  0  2  0  0  6  6  4  4 10  6 14  4  8  2  0  6  2 12  0  8  2  2 12  6  6  4  6  6  4 10  2 10 10  4  0 12
 0  0  2  2 12  6  6  0 12  2 14 12  2 12 10  4 14  0 12 12  6  2 14  2  6 14 10  0  2  0 10 14 10  8  6 12  2 10
 0  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8  8  8  8  0  0  8  0  8  0  0  8  8  0  0  8  0  8  0  8  8  8  0
 0  0  0  0  8  0  0  8  0  8  8  0  0  8  8  8  8  8  8  8  8  8  8  0  0  0  0  8  0  0  0  0  8  0  8  0  8  8
 0  0  0  0  0  8  0  0  0  8  8  8  8  0  0  8  0  8  0  8  8  0  0  8  8  8  0  0  0  8  0  0  8  0  8  8  0  8
 0  0  0  0  0  0  8  0  8  0  8  8  0  8  0  8  8  0  0  0  8  0  8  0  8  0  8  0  0  8  0  8  8  0  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+56x^31+237x^32+254x^33+612x^34+914x^35+1838x^36+2884x^37+2819x^38+2920x^39+1878x^40+800x^41+603x^42+316x^43+138x^44+28x^45+52x^46+16x^47+4x^48+2x^49+8x^50+2x^51+1x^54+1x^58

The gray image is a code over GF(2) with n=304, k=14 and d=124.
This code was found by Heurico 1.16 in 2.48 seconds.