The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  4  2  4  2  1  0  2  0  2  2  1  1  4  2  4
 0 12  0  4  0  0  4 12  0  8  4  0  4  8  4  4  0  8  0  4 12  8 12  8 12  8 12 12  4  8  0 12  4 12 12 12  8  8  4  4
 0  0 12  4  0 12  4  0  0  4  0  8 12 12  8  4  8  4  4  4  8  0  4  4  0  4  0  0 12  8  4  8  0  8  8  0  8  4  0  4
 0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  0  0  0  8  8  0  8  0  8  8  0  8  0  8  8  0  0  8  8  0  0  0  8  8  8
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  0  8  8  8  0  8  0  8  8  0  0  0  0  0  0  0  8
 0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  8  8  0  8  8  8  8  8  8  8  0  8  0  8  8  0  8  8
 0  0  0  0  0  0  8  0  0  8  8  8  0  0  0  0  8  8  0  8  0  8  8  8  0  0  8  8  0  0  0  8  0  8  8  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  0  0  8  8  8  8  8  0  0  0  0  8  0  0  0  8  8  0  8  8  0
 0  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  0  0  8  8  0  0  8  0  8  8  8  8  8  0  8  0  0  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+248x^32+462x^34+1063x^36+512x^37+2456x^38+1536x^39+3784x^40+1536x^41+2564x^42+512x^43+1086x^44+376x^46+173x^48+30x^50+43x^52+2x^56

The gray image is a code over GF(2) with n=320, k=14 and d=128.
This code was found by Heurico 1.16 in 84.6 seconds.