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 X^2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2+X  2 X+2  2 X^2+X X^2  X X^2+2 X^2+X X+2 X^2 X^2+X+2 X^2+2  2  0 X+2 X^2+X+2 X^2+X+2 X^2+X X^2  2  0  X X^2+2  0 X+2 X^2 X^2+2  X  X  2 X^2+X X^2+X  2 X+2 X^2+X+2  2  2
 0  0  X  X X^2+2 X^2+X X^2+X+2 X^2 X^2  X X^2+X  0  2 X^2+X+2 X^2  X X+2 X^2+X X^2+2  0 X^2+X+2 X^2+2 X^2+2 X^2+X  X X+2 X^2+2  0  2 X^2+X+2  0  X X+2  2 X^2+2 X^2+X  2  2 X^2+X X^2 X^2  0 X+2 X+2 X^2+X  X X^2+X+2 X^2+2  0 X^2+X+2  2 X^2  0

generates a code of length 53 over Z4[X]/(X^3+2,2X) 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 0.078 seconds.