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

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+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.