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

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

Homogenous weight enumerator: w(x)=1x^0+136x^50+96x^51+158x^52+40x^54+32x^55+30x^56+16x^58+2x^60+1x^64

The gray image is a code over GF(2) with n=416, k=9 and d=200.
This code was found by Heurico 1.16 in 0.109 seconds.