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

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

Homogenous weight enumerator: w(x)=1x^0+244x^40+426x^42+24x^43+914x^44+216x^45+1662x^46+632x^47+5771x^48+1144x^49+10744x^50+1224x^51+5597x^52+648x^53+1824x^54+168x^55+803x^56+40x^57+398x^58+221x^60+50x^62+12x^64+3x^68+1x^72+1x^76

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 19.5 seconds.