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  X
 0  X  2 3X+2  0 3X+2  2 3X  0 3X+2 3X  2  0 3X+2  2 3X 3X  0  2 3X+2 2X X+2 2X+2 3X  0 3X+2  2 3X 2X X+2 2X+2  X  0 3X+2  2  X 2X X+2 2X+2 3X 2X X+2 2X+2  X 2X 2X X+2  X  0 2X X+2 X+2  2
 0  0 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X 2X
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X 2X  0 2X  0 2X 2X  0 2X  0 2X 2X  0 2X  0  0  0
 0  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0  0  0 2X  0  0 2X 2X 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+61x^50+138x^52+640x^53+122x^54+52x^56+9x^58+1x^104

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 0.125 seconds.