The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  0  2  0  1  2  2  1  2  1  1  1  1  4  1 12  8  4  2  1
 0  2  0  2  0  0  2 10  4  4 14  6 12 10  8 14 12  6 14  6  0  0 14  2  2  2  4  4 10  0  4 14 14  2  4 12  2  2  2  8
 0  0  2  2 12  6  6 12  4  2  6  0 14  2 12  4  0  2  8  0  6  2  4  4  8 10 10  8 10  0  6  8 10  2  0  2  8  6  6  0
 0  0  0  4  0  0  4  0  0  8  4  8  8 12  8  0  8  4  8  0  8  8  0 12 12  0  4 12 12  4 12 12  0  8 12 12  4 12  4  4
 0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  0  0  0  8  8  0  0  0  8  8  0  8  0  8  8  8  0  8  0  8  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8  8  8  8  0  8  8  8  0  8  8  8  0  8  0
 0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  0  0  8  8  8  8  0  0  0  8  8  0  8  8  8  0  0  0  8  8  8  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+72x^32+164x^33+340x^34+824x^35+1132x^36+2576x^37+3372x^38+5202x^39+5523x^40+5162x^41+3395x^42+2478x^43+1137x^44+766x^45+295x^46+190x^47+64x^48+34x^49+21x^50+10x^51+7x^52+2x^53+1x^54

The gray image is a code over GF(2) with n=320, k=15 and d=128.
This code was found by Heurico 1.16 in 10 seconds.