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

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

Homogenous weight enumerator: w(x)=1x^0+32x^50+24x^51+92x^52+284x^53+28x^54+4x^55+8x^56+4x^57+28x^58+4x^59+2x^68+1x^72

The gray image is a code over GF(2) with n=424, k=9 and d=200.
This code was found by Heurico 1.16 in 0.11 seconds.