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

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

Homogenous weight enumerator: w(x)=1x^0+81x^44+82x^46+32x^47+171x^48+608x^49+126x^50+608x^51+149x^52+32x^53+94x^54+31x^56+18x^58+9x^60+4x^64+1x^72+1x^84

The gray image is a code over GF(2) with n=400, k=11 and d=176.
This code was found by Heurico 1.16 in 0.164 seconds.