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

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

Homogenous weight enumerator: w(x)=1x^0+143x^44+20x^45+218x^46+76x^47+448x^48+684x^49+1076x^50+648x^51+366x^52+92x^53+116x^54+12x^55+98x^56+4x^57+52x^58+27x^60+10x^62+4x^64+1x^80

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 1.66 seconds.