The generator matrix

 1  0  1  1  1 14  1  1  4  1  1  4 10  1  1  1  2  1 10  1  1  6  1  1  1  1  1  8  2  1  1  2  8  1  1  1  1  1
 0  1  1  4  7  1  2  3  1  5  6  1  1  9 14  2  1 12  1 15  7  1 12  5  6  1  8  1  6 11  6  4  2  1 11  7 13  0
 0  0  2  2  2  4  2  0  2  0  8 12  6  6 10 12  2  0  0 14 12  6 14  6  6 12 12 12  6  2  8 14 10  4 12  0  4  8
 0  0  0  8  0  0  8  0  0  8  8  8  8  0  8  0  0  8  0  8  8  0  0  8  0  8  0  8  0  8  0  8  0  0  8  0  8  8
 0  0  0  0  8  0  0  0  8  8  8  8  0  0  8  8  0  0  8  0  8  0  0  8  8  0  8  8  0  8  0  0  0  8  0  8  0  8
 0  0  0  0  0  8  8  8  0  0  8  0  0  8  0  8  8  0  8  0  8  0  0  8  0  8  0  8  0  0  8  8  8  0  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+46x^32+232x^33+598x^34+1408x^35+1619x^36+3160x^37+2386x^38+3124x^39+1694x^40+1234x^41+460x^42+258x^43+88x^44+44x^45+10x^46+8x^47+7x^48+2x^49+2x^50+2x^51+1x^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 1.62 seconds.