The generator matrix

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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+165x^42+260x^43+660x^44+768x^45+1269x^46+2396x^47+3335x^48+5272x^49+4627x^50+5244x^51+3220x^52+2544x^53+1312x^54+644x^55+523x^56+248x^57+157x^58+32x^59+64x^60+19x^62+4x^64+3x^66+1x^72

The gray image is a code over GF(2) with n=400, k=15 and d=168.
This code was found by Heurico 1.16 in 14.1 seconds.