The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+225x^32+300x^33+840x^34+1096x^35+1786x^36+2696x^37+2526x^38+2708x^39+1877x^40+1132x^41+636x^42+224x^43+219x^44+32x^45+62x^46+4x^47+17x^48+3x^52

The gray image is a code over GF(2) with n=304, k=14 and d=128.
This code was found by Heurico 1.16 in 2.64 seconds.