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  X  0  X  0  1  1  X  1  X  1  X  1  1  2  X  1  X  1  1  2  1  1  1  0  1  1  1
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2  0 X+2 X+2 X+2  2  0  0  0  X X+2 X+2  2  2  0  X  X X+2  X  X  X  X  2  X  X  0  X X+2  2  X  X  2  X  X  2  X  X X+2  X  0
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  0  2  0 X+2 X+2  2 X+2  2  X  2  2  X  X  X  0  X  2  0  X  X X+2  X  2  0 X+2 X+2  2 X+2  X  0  0 X+2  2  0  X  2  2  X  0
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0  2 X+2  0  X X+2  X  2  X  0 X+2 X+2  X  2  0  X X+2  2 X+2  2  X  0  X  X  2 X+2  0  0  0  0 X+2  2  0  0  0  2  0  0  2  2
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  2  0  0  0  2  2  0  2  0  2  0  0  2  2  2  2  2  0  2  2  0  0  0  2  0  0  0  2  0  0  0
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  0  0  0  2  2  0  0  0  0  0  2  2  2  0  2  2  0  2  0  2  0  2  0  2  0  0  2  2  0  2  2  0  2  0  2  2
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  2  0  2  0  0  0  2  2  2  0  2  2  0  0  0  2  2  0  2  2  2  2  0  2  0  2  2  2  0  0  2  2  2  0  0  0  0  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+125x^48+4x^49+282x^50+44x^51+386x^52+164x^53+492x^54+300x^55+619x^56+300x^57+468x^58+164x^59+304x^60+44x^61+178x^62+4x^63+128x^64+48x^66+30x^68+2x^70+6x^72+2x^74+1x^88

The gray image is a code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 1.08 seconds.