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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+246x^44+8x^45+232x^47+414x^48+784x^49+768x^50+784x^51+383x^52+232x^53+8x^55+204x^56+26x^60+5x^64+1x^84

The gray image is a code over GF(2) with n=400, k=12 and d=176.
This code was found by Heurico 1.16 in 86.7 seconds.