The generator matrix

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

generates a code of length 40 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+84x^32+32x^33+316x^34+296x^35+1302x^36+1872x^37+4454x^38+4440x^39+7158x^40+4480x^41+4532x^42+1880x^43+1200x^44+272x^45+280x^46+40x^47+89x^48+16x^50+18x^52+2x^54+4x^56

The gray image is a code over GF(2) with n=320, k=15 and d=128.
This code was found by Heurico 1.16 in 7.07 seconds.