The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+191x^52+55x^56+5x^60+4x^64

The gray image is a code over GF(2) with n=424, k=8 and d=208.
This code was found by Heurico 1.16 in 25.3 seconds.