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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+75x^48+86x^50+16x^51+230x^52+80x^53+246x^54+160x^55+324x^56+160x^57+210x^58+80x^59+174x^60+16x^61+98x^62+66x^64+20x^68+5x^72+1x^88

The gray image is a code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.382 seconds.