The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  0  2  4  2  1  1  2  8  2  8  2  1  1  1  1 12  2  4  8  1  4
 0  2  0  6  4  6 12  2  8  6 12 14  0  2  4 14  6  2  6  2 14  2 14  8 10 10  2  6  2  2  6  6  4  8  2 14  4  4  2  4
 0  0 12  0  4  0  0  0  8  4  4  4  4 12  8  0  0  0 12  4 12  8  8 12  4  4  0 12 12 12  0  8 12  0  0 12  4  8  4  8
 0  0  0 12  0  0  0  4 12  4 12  8 12  8 12 12  8 12  4 12  0 12 12  0 12 12 12  4  8  0  8  0 12  4  0  0  8 12  4 12
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  0  8  0  8  0  8  8  8  0  0  8  8  0  8  0  8  8  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  0  8  8  0  0  0  8  8  8  0  0  0  8  8  0  8  0  0  8  0  8  8
 0  0  0  0  0  0  8  0  0  0  0  0  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  8  0  8  0  0  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  0  0  8  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+223x^32+96x^33+620x^34+604x^35+1883x^36+2188x^37+3780x^38+4316x^39+5271x^40+4108x^41+4124x^42+2420x^43+1746x^44+516x^45+524x^46+84x^47+198x^48+4x^49+40x^50+19x^52+3x^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 52.7 seconds.