The generator matrix

 1  0  1  1  1  4  1 10  1  1  1  6  1  4  2  1 10  1  1  1  1  1  1  6  6  1  1 12  2  1  1  6  1  1  8  8 12  1  1  1
 0  1  1  0 11  1 10  1  5  6  7  1 15  1  1  8  1 15 12 13 14 12 13  1  1  7 10  1 12  7 14  1  0 15  1  1  1  6  1  8
 0  0  2  6  4  6 10 10  0  0  2  8  2 10  2  0 12 12 10  6 12 12  0 10 12 14  6 14  2  0 10 14  8 10 14  8 12  2  6  0
 0  0  0 12  0  4 12  4  0  0  8  0  4  0  8  4 12 12  4  4  0  4  4 12 12 12  0  8  4  8  0  8  0 12  4  4 12 12 12 12
 0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  0  8  0  0  8  8  0  0  8  8  8  0  0  8
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  8  0  0  0  8  8  8  8  8  8  8  0  8  0  0  0  0  8  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  0  0  8  0  8  0  0  0  0  8  8  0  8  8  0  8  8  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+61x^32+186x^33+456x^34+922x^35+2043x^36+4320x^37+7499x^38+11452x^39+11605x^40+11520x^41+7601x^42+4352x^43+1963x^44+828x^45+415x^46+164x^47+65x^48+38x^49+27x^50+6x^51+6x^52+4x^53+2x^54

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 25.3 seconds.