The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+87x^32+468x^33+1151x^34+2502x^35+3394x^36+6170x^37+5321x^38+6048x^39+3519x^40+2566x^41+937x^42+366x^43+157x^44+40x^45+15x^46+12x^47+9x^48+2x^49+1x^52+2x^53

The gray image is a code over GF(2) with n=304, k=15 and d=128.
This code was found by Heurico 1.16 in 5.03 seconds.