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

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

Homogenous weight enumerator: w(x)=1x^0+221x^32+390x^34+128x^35+827x^36+644x^37+2128x^38+2292x^39+3130x^40+2312x^41+2154x^42+648x^43+805x^44+116x^45+326x^46+4x^47+192x^48+56x^50+7x^52+2x^54+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 4.39 seconds.