The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+111x^32+56x^33+266x^34+168x^35+632x^36+720x^37+2454x^38+1608x^39+4316x^40+1600x^41+2546x^42+760x^43+582x^44+176x^45+210x^46+24x^47+106x^48+8x^49+28x^50+10x^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 3.05 seconds.