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

generates a code of length 53 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+25x^50+80x^51+38x^52+736x^53+38x^54+80x^55+25x^56+1x^106

The gray image is a code over GF(2) with n=424, k=10 and d=200.
This code was found by Heurico 1.16 in 0.172 seconds.