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  0  1  1  1  1  1  1  X  0  1  1  1  0  0  1  2  1  X  X  1  X  X  1  0  X  1  0
 0  X  0  X  0  0  X X+2  0  2 X+2  X  0  X  X  0  2  2 X+2  X  0  0  X  2  2  X  0 X+2  0  2 X+2  2 X+2  X  0  2  2  0 X+2  X  2  2  X  0  X  X  X  X X+2  2  2  X  0  2  0  X
 0  0  X  X  0 X+2  X  0  2  X  0  X  0 X+2  2 X+2  X  X  2  0  2  0 X+2  2  2 X+2  X  X X+2  X X+2  X X+2 X+2  0  0  X  X  2  2  X  X  0 X+2 X+2  2 X+2  X  2  X  X X+2  X  2  2  2
 0  0  0  2  0  0  0  0  2  2  2  0  2  0  2  0  0  0  2  0  2  2  2  0  0  2  0  0  0  2  2  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  0  0  0  2  0  2  2  0  2  2
 0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  0  2  0  2  2  2  2  0  0  2  0  2  0  2  2  2  2  2  0  0  2  2  2  0  0  0  0  2  0  0  2  2  0  2
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  2  2  2  0  2  0  0  0  2  2  0  2  2  0  0  0  0  2  0  0  0  2  2  2  0  0  2  0  2  0  2  2  0  0  0  0  2  2  0  2  2  2
 0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  0  0  0  2  0  2  2  0  0  0  0  0  2  0  2  0  2  0  2  2  2  0  0  2  0  0  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  2  0  2  2  0  2  0  2  2  0  0  2  0  2  2  2  0  2  2  2  0  0  2  0  0  2  2  0  0  2  0  2  0  0  2  0  0  2  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+185x^48+4x^49+218x^50+44x^51+398x^52+164x^53+490x^54+300x^55+572x^56+300x^57+476x^58+164x^59+340x^60+44x^61+172x^62+4x^63+136x^64+42x^66+27x^68+10x^70+2x^72+2x^76+1x^84

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 18.1 seconds.