The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+53x^32+420x^33+894x^34+1866x^35+2918x^36+4898x^37+6966x^38+9658x^39+10094x^40+9702x^41+7048x^42+5154x^43+2886x^44+1646x^45+682x^46+406x^47+172x^48+38x^49+24x^50+4x^51+4x^52+2x^58

The gray image is a code over GF(2) with n=320, k=16 and d=128.
This code was found by Heurico 1.16 in 36.3 seconds.