The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  8  1  8  1  2  1  1  2  1  2  1  1  2  0  1  2  0  1  2  1  1  1
 0  2  0  6  0  6  8  6 14  0  0 14  6  4  2  4  6  2  2 10  2 14  6  4  8  6  2 10 14  0  6  2 14 14  4  6  0 14  4  0
 0  0 12  0  0  0 12  0  0  8  4  4  4  0  8  8 12  4 12 12  8  4  0 12  4  4 12  8 12  4  8  8  0  0 12  4  4  8  4  0
 0  0  0 12  0  0  0  4  8 12  4 12  0  4  0  8  4  8  0 12  4  8 12 12 12  4  8  4  4  0 12  8  4 12  4  4  0  4  4  8
 0  0  0  0 12  0  4  4 12  4  0  4  4  8  4 12  0  4  8  8  0  8  4 12 12  0 12  4  8  4 12  0  8  0  8 12 12 12 12  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  0  8  8  0  0  0  8  0  8  8  0  8  8  8  8  8  0  8  8  8  0  8  8  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+28x^32+116x^33+190x^34+400x^35+564x^36+1032x^37+1901x^38+2568x^39+2843x^40+2576x^41+1906x^42+996x^43+542x^44+360x^45+150x^46+96x^47+51x^48+44x^49+12x^50+4x^51+2x^52+1x^54+1x^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 3.03 seconds.