The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+133x^32+16x^33+224x^34+176x^35+775x^36+400x^37+2208x^38+2480x^39+3586x^40+2480x^41+2208x^42+400x^43+747x^44+176x^45+224x^46+16x^47+102x^48+29x^52+2x^56+1x^60

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 4.95 seconds.