The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+237x^32+344x^33+724x^34+1080x^35+1945x^36+2412x^37+2958x^38+2464x^39+1927x^40+1024x^41+644x^42+328x^43+203x^44+28x^45+46x^46+3x^48+12x^50+4x^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 3.15 seconds.