The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+63x^32+222x^33+324x^34+612x^35+892x^36+1356x^37+1391x^38+1378x^39+750x^40+578x^41+308x^42+144x^43+80x^44+48x^45+20x^46+10x^47+6x^48+4x^49+4x^50+1x^54

The gray image is a code over GF(2) with n=304, k=13 and d=128.
This code was found by Heurico 1.16 in 0.616 seconds.