The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  2  1  1  X  1  1  X  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  0  X  X  2  0 X+2  2  X  2  1  1
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  2 X+3  1  X  1  1  0 X+2 X+1  3  0 X+2 X+1  3  2  X  2  X X+3  1 X+3  1  0 X+2  X  2  X  X  1  1  1  1  0  0  2
 0  0  2  2  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2  2  0  0  2  0  2  2  0  2  0  2  0  0  2  2  0  0  2  2  2  2  2  2  2  0  0  0  0  2  0  2

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

Homogenous weight enumerator: w(x)=1x^0+66x^52+48x^54+9x^56+1x^60+2x^64+1x^68

The gray image is a code over GF(2) with n=212, k=7 and d=104.
This code was found by Heurico 1.16 in 0.0524 seconds.