The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^44+106x^45+200x^46+296x^47+416x^48+630x^49+741x^50+656x^51+414x^52+262x^53+135x^54+66x^55+63x^56+22x^57+7x^58+4x^59+6x^60+2x^61+4x^62+2x^63+4x^64+1x^68+2x^69+1x^78

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 0.358 seconds.