The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1  2  1  1 2X  1  1 3X+2  1  1 2X+2  1  1 3X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  0  X X+2 2X+2  1  1  1  1  1
 0  1 X+1 X+2 2X+3  1  X 3X+3  1  2 2X+1  1 2X X+1  1 3X+2  3  1 3X X+3  1 2X+2  1  1  0 X+2  2 3X 2X+2  0 3X+2 2X+2  X X+1  3 X+3  1 3X+1  3 X+3  1  1 2X  1  1  1  X 2X  X X+2  X 2X
 0  0 2X+2  2 2X 2X+2 2X+2  2  2 2X  0 2X 2X+2  0 2X+2  0 2X+2  0 2X 2X  2  2  2 2X 2X 2X+2 2X+2  2  0  2 2X 2X+2  0 2X  2  0 2X+2  2  0 2X+2 2X 2X 2X  2 2X+2 2X  2  2  2  0 2X  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+328x^50+120x^51+210x^52+48x^53+248x^54+24x^55+43x^56+1x^68+1x^76

The gray image is a code over GF(2) with n=416, k=10 and d=200.
This code was found by Heurico 1.16 in 8.45 seconds.