The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+4x^50+36x^51+182x^52+16x^53+2x^54+8x^55+1x^56+1x^58+4x^59+1x^66

The gray image is a code over GF(2) with n=416, k=8 and d=200.
This code was found by Heurico 1.16 in 0.109 seconds.