The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1  1 12  1  1  1 14 10  1  1  1  0  1  1  1  1  1  1  1  2  1  1  0  1  1  2  2
 0  1 11  6 13  1  7  6  1  1  1  8 12  1  3 10 13  1  1  0  6 11  1  3  8  2  9 14  7  7  1 14 12  1  7 10 14 14
 0  0 12  0  4  0  4  8 12 12  4  4  0  0  0  8  8  0  4  4  4  8 12  4  0  8  8  4  8  0 12 12 12  4 12  4  8  4
 0  0  0 12  0  0  0  0  0  8  8  8  8  0  0  0  4  4 12 12 12 12  4  4 12  4  8  8  4  4  0  8 12  4 12 12 12  8
 0  0  0  0  8  0  8  0  0  0  8  0  8  8  8  8  8  0  8  8  0  0  0  0  0  8  8  8  0  8  8  8  0  8  0  8  0  0
 0  0  0  0  0  8  8  8  8  8  8  8  0  8  0  8  0  0  0  8  8  8  8  8  8  8  0  0  8  8  0  8  8  0  0  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+202x^32+108x^33+540x^34+1064x^35+1932x^36+2932x^37+2900x^38+2928x^39+1880x^40+1044x^41+552x^42+104x^43+122x^44+12x^45+36x^46+21x^48+4x^50+2x^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 1.87 seconds.