The generator matrix

 1  0  1  1  1 14  1  1  6  1  8  1  4  1  1  1  1  2 12 10 14  2  1  1  1  1  8  1  6 14  1  1  1  0  1  6  2  1  2  1
 0  1 11 14  5  1  0  3  1  6  1 13  1  4 15 10  1  1  1  1  1  1  7  9  2  8  1 12  1  1 13 11  4  1 11  1 14  6  0  0
 0  0 12  4  0  4 12  0  0  8 12 12  4  4  8  0 12  4  0  0  4  4 12  0 12  4  4  8  0 12 12  4  4  8  4  0  4  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  0  0  0  8  8  8  0  0  8  8  0  8  8  8  8  0  0  0  0  0
 0  0  0  0  8  0  0  0  0  8  8  0  0  0  8  0  8  8  8  0  8  0  8  0  8  8  0  0  0  0  8  8  8  8  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  0  8  0  0  0  0  8  0  0  8  8  0  0  0  8  8  8  8  0  8  0  8  8  8  0  0  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  8  0  0  0  8  8  8  8  0  8  0  8  8  0  0  0  8  8  8  0  0  0  0  8  0
 0  0  0  0  0  0  0  8  0  8  8  0  0  0  0  0  8  0  0  8  0  8  8  8  8  8  0  8  8  0  0  0  0  8  0  0  8  0  0  8
 0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  8  0  8  0  0  0  8  8  0  8  8  8  0  0  0  0  8  8  8  0  8  8

generates a code of length 40 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+34x^30+30x^31+124x^32+228x^33+327x^34+852x^35+1827x^36+4548x^37+7809x^38+10696x^39+12523x^40+10748x^41+7843x^42+4612x^43+1814x^44+812x^45+316x^46+186x^47+79x^48+48x^49+45x^50+8x^51+15x^52+9x^54+1x^56+1x^58

The gray image is a code over GF(2) with n=320, k=16 and d=120.
This code was found by Heurico 1.16 in 24.2 seconds.