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

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+30x^50+90x^51+81x^52+620x^53+81x^54+90x^55+30x^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 0.094 seconds.