The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  0  1  1  0
 0  X  0  X  0  0  X  X  0  0  X  X  0  2 X+2  X X+2  2 X+2  2  X  0  2 X+2 X+2  0  2  X  2  0 X+2 X+2  X  X  2  0  2  2  0  2  X X+2  2 X+2  2  0  0  0  X  0 X+2  X
 0  0  X  X  0 X+2  X  0 X+2  0  X  0  2  X  0  X  2  0  X X+2 X+2  0  X  2  0  2  X  X  0 X+2 X+2  2  2  2 X+2  2 X+2  2 X+2  0  0  2 X+2  2 X+2  X X+2  X  0  0  2  0
 0  0  0  2  0  0  2  0  0  2  0  2  2  2  2  2  0  0  0  0  2  0  2  2  0  2  2  0  2  2  0  2  0  2  2  0  0  0  2  0  2  2  2  0  0  2  0  0  0  0  0  2
 0  0  0  0  2  0  2  2  2  2  0  0  0  2  2  2  2  0  2  2  0  2  0  0  0  0  2  2  2  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  0  2
 0  0  0  0  0  2  0  0  2  2  2  2  2  0  2  2  2  2  2  0  2  2  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  0  0  0  0  2  0  0  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 48.

Homogenous weight enumerator: w(x)=1x^0+234x^48+128x^50+320x^52+128x^54+200x^56+12x^64+1x^96

The gray image is a code over GF(2) with n=208, k=10 and d=96.
This code was found by Heurico 1.16 in 19.2 seconds.