The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  4  4  2  4  1  8  4  2  0  2  2  2  2
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  8 12  0  4  4  0  4  4  8  4  8  4 12  0  8  4  4  8  4  8 12 12 12
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4  0  4 12  8  4  0 12  4 12  0  4  0 12  8  4  8 12  0  8  0 12  8 12
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  8  4 12  8  0  0  0  0  0  4  4  8  4 12  4  4 12  0  4  8  4  0  0 12
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  8  0  8  8  0  8  8  0  0  8  8  8  0  0  0  8  8  8  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  0  0  0  0  0  8  8  0  0  8  8  8  8  8  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  0  8  0  8  8  8  8  8  8  0  8  0  0  0  8  8  0  0  8  0  0  8
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  8  0  8  8  0  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+210x^32+494x^34+32x^35+1030x^36+544x^37+2538x^38+1472x^39+3790x^40+1472x^41+2534x^42+544x^43+1014x^44+32x^45+414x^46+205x^48+36x^50+20x^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 3.89 seconds.