The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2+2  1  X  2  1  X X^2  1  1  1  1  1  X  X  X  X  1  X  X  0 X^2+2 X^2  X  2  0  1  1  X X^2  1  1  1  1  1
 0  X 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 X^2+X  X X+2  X  0 X^2+X+2  X X^2+X  X  X X^2+2 X+2  2 X^2 X^2+X+2 X^2+2  0  2 X^2  X X^2+X X+2  X  X X^2+2 X^2+X+2  X X^2  0  2  X  X X^2+2 X^2  0  2  0

generates a code of length 53 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+38x^52+40x^53+36x^54+8x^55+1x^56+2x^58+1x^62+1x^70

The gray image is a code over GF(2) with n=424, k=7 and d=208.
This code was found by Heurico 1.16 in 0.079 seconds.