The generator matrix

 1  0  1  1  1  2  1  1  0  1  1  0  0  1  1  1  1  0  2  1  1  1  1  0  2  X  X X+2 X+2  2 X+2  X  X X+2  X  1  1  1  1  1  1 X+2  X  1  1  X  1  2  1  1  1  2
 0  1  1  0 X+1  1 X+3  0  1  2  1  1  1 X+1 X+2 X+1  X  1  1 X+2  3 X+2  1  1  1  1  1  1  1  X  1  1  1  1  1  0 X+2 X+1  1 X+3  0  1  1  0  1  1  3  1  3  2 X+2  X
 0  0  X  0  0  0  0 X+2 X+2 X+2  X X+2  2 X+2  X X+2  X  2 X+2  2  2  2  2  X X+2  0  0  X X+2  X  0  2  2  0  2  0  0  X  X  2  X X+2  X  2 X+2  0  0  X  X  2  X  X
 0  0  0  X  2 X+2 X+2 X+2 X+2  2  X  0  0  X X+2  0  2  X  2  X X+2  0  2  2  X  X X+2  X  X  0  0  2  X  2  0 X+2  2  X  2  X X+2 X+2  0  0 X+2  0 X+2  2  0  2  2  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+201x^48+234x^50+224x^52+172x^54+150x^56+10x^58+20x^60+10x^64+2x^72

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 0.0945 seconds.