The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+76x^50+8x^52+16x^54+6x^56+16x^58+4x^62+1x^64

The gray image is a code over GF(2) with n=208, k=7 and d=100.
This code was found by Heurico 1.16 in 6.39 seconds.