The generator matrix

 1  0  0  0  1  1  1  2 2X+2  2  1  1  1  1 3X+2  1 X+2  1 2X+2  1  1  1  2 3X+2  2  X 3X+2 3X+2  1  1  1  1  0 2X 3X+2  0  1  1 3X  1  1  1 X+2  1 3X  2  1  1 3X  1
 0  1  0  0 2X  1 2X+1  1  1  1 3X+3 2X X+3 3X  2 X+2  1 3X+1  0 X+2 2X+1 X+3  1  X  X  1  1  1 X+3 2X 2X+2  X 2X+2  1 2X  1 3X  1  1 2X+3 X+2 X+1  1 2X  1  1 3X+1  X 3X+2  2
 0  0  1  0 2X+1  1 2X 2X+1  0 X+1  1 X+2 3X X+1  1 X+3 3X+3 2X+2 X+2  2 3X 3X+1 X+2  1  1  3 X+2  X 3X+3  3  X 2X+1  1 2X+1  1 2X+2 2X  0 3X 3X+3 2X+1 2X 3X+1 2X+2  0 2X+1 3X+3 2X+2  1 3X+2
 0  0  0  1  1 2X 2X+1 2X+1  3 3X X+3 3X+3 3X 3X+2 2X+3  1  X  2  1 3X+1 2X+3  1 X+3  3  2 3X+3 2X  1 2X 3X+1  0 3X+2  X 3X+1 3X+1 3X+2  3 X+3 3X+1  3  3 3X X+1 3X+2 2X+2  0 3X+3 3X  X  0

generates a code of length 50 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+362x^44+1770x^45+3255x^46+5520x^47+7699x^48+9350x^49+9829x^50+9458x^51+7608x^52+5526x^53+2905x^54+1454x^55+512x^56+186x^57+67x^58+14x^59+10x^60+8x^62+2x^63

The gray image is a code over GF(2) with n=400, k=16 and d=176.
This code was found by Heurico 1.16 in 24.5 seconds.