The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+398x^44+1798x^45+3248x^46+5696x^47+7084x^48+9688x^49+9780x^50+9502x^51+7512x^52+5864x^53+2818x^54+1424x^55+443x^56+148x^57+64x^58+50x^59+8x^60+6x^61+2x^62+2x^64

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 25.5 seconds.