The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^52+8x^54+3x^56+1x^60+1x^68

The gray image is a code over GF(2) with n=208, k=6 and d=104.
This code was found by Heurico 1.16 in 0.0318 seconds.