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  X  1  1 2X+2 2X+2
 0  2  0 2X+2  0  0 2X+2  2  0  0 2X+2  2  0  0 2X+2  2  0 2X+2 2X 2X+2  2 2X  0  2  2 2X 2X+2 2X 2X+2 2X 2X+2 2X  0 2X+2  2  0 2X 2X  2  2 2X+2 2X 2X  2 2X+2 2X+2  0  0 2X  0 2X 2X+2  2
 0  0  2 2X+2  0  2 2X+2  0  0  2 2X+2  0  0  2 2X+2  0 2X  2 2X+2  0  2 2X 2X+2 2X 2X+2  0 2X  2  2 2X  0 2X+2 2X  0 2X+2 2X+2 2X  2 2X  2  2  0  2 2X  0 2X 2X 2X 2X+2 2X+2 2X+2 2X+2  0
 0  0  0 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X 2X  0 2X 2X  0  0  0 2X  0 2X  0 2X  0 2X
 0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X 2X  0 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+70x^50+80x^51+198x^52+352x^53+188x^54+80x^55+23x^56+30x^58+1x^60+1x^100

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.