The generator matrix

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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+91x^40+12x^41+264x^42+84x^43+916x^44+344x^45+2266x^46+1272x^47+5273x^48+2416x^49+6916x^50+2336x^51+5383x^52+1256x^53+2328x^54+392x^55+742x^56+68x^57+244x^58+12x^59+110x^60+14x^62+20x^64+7x^68+1x^72

The gray image is a code over GF(2) with n=400, k=15 and d=160.
This code was found by Heurico 1.16 in 15.3 seconds.