The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  1  0  1  1  1  2  1  0  1  X  1  1 X+2  1  1  1  1  1  1  0  1  1  0  1 X+2  1  1  1  1  1 X+2  1  2  1  1  2  1  1  1  1  1  0  1
 0  1  1 X+2 X+3  1  0 X+1  1  X  3  1 X+3  2  1  0 X+1  1  1 X+2  1  X  1  3  3  1  2 X+1  X  3  2 X+2  1  X  1  1 X+1  1 X+3  0  3  X  3  1  3  X  X  X  X X+1  1  2 X+1  3  X  0
 0  0  X  0 X+2  0 X+2  0 X+2  X  2  X X+2 X+2  0  2  0 X+2  X  0 X+2 X+2 X+2  2 X+2  0  X X+2 X+2  2  0  2  0  2 X+2  2  2  0  0 X+2  0 X+2  0 X+2 X+2  X  X  0  X  X  2  X  X  2  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  0  2  2  0  2  0  2  2  2  0  2  0  0  0  2  0  2
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  0  2  0  0  2  2  2  2  2  2  2  2  2  2  0  2  2  0  2  2  0  0  2  2  2  0  0  0  2  0  2  2  2  2  2
 0  0  0  0  0  2  0  0  0  2  2  0  2  2  0  2  2  2  0  0  0  0  0  0  2  0  2  0  2  0  2  0  0  0  2  0  2  2  2  0  2  0  0  0  2  2  0  2  2  0  0  2  2  0  0  2
 0  0  0  0  0  0  2  0  2  0  0  2  0  2  0  0  0  0  2  0  2  0  0  0  0  0  2  0  2  0  2  2  2  0  2  2  2  0  2  0  0  0  2  2  2  0  2  2  2  0  2  0  2  2  2  2
 0  0  0  0  0  0  0  2  2  0  2  2  0  0  0  0  0  2  0  2  0  2  2  2  0  2  0  0  2  0  0  2  2  2  0  2  0  2  2  2  0  2  2  2  2  0  0  0  0  2  0  2  0  0  0  0

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+193x^48+36x^49+382x^50+232x^51+733x^52+544x^53+832x^54+728x^55+996x^56+728x^57+788x^58+536x^59+583x^60+224x^61+360x^62+40x^63+133x^64+4x^65+62x^66+43x^68+8x^70+4x^72+1x^76+1x^80

The gray image is a code over GF(2) with n=224, k=13 and d=96.
This code was found by Heurico 1.16 in 3.47 seconds.