The generator matrix

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

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+276x^50+56x^52+120x^54+4x^56+52x^58+3x^64

The gray image is a code over GF(2) with n=208, k=9 and d=100.
This code was found by Heurico 1.16 in 13.5 seconds.