The generator matrix

 1  0  1  1  1 X+2  1  1  2  X  1  1  1  X  1 X+2  1  1  1  1  2  2  1  1  1  0  2  1  1  1  1  1  1 X+2  0  1  1  2  1  1  2  1  1 X+2  1  1  2  1  1  1  2  1  1  1  1  1
 0  1  1  0 X+3  1  X X+1  1  1 X+2  3 X+1  1 X+2  1  2  3  X X+1  1  1  0  X  3  1  1 X+3  3  1  2  2  0  1  1  1 X+1  1  3  X  1  2 X+3  1  0  2  X X+3  2 X+1  1  0  2  2 X+3 X+2
 0  0  X  0 X+2  0  0  0  2  2  0  2  X X+2  X X+2  X X+2  X  2 X+2  X X+2  X  0  2  X  0 X+2  0  2  X X+2  X  X  2  X  2  2  0  0  X  X  0  0  0  0  X  2 X+2 X+2 X+2  2  2  0  2
 0  0  0  X  0  0  X  2 X+2  X  0  0  X  0 X+2 X+2  2  X  0 X+2  2 X+2  X  0 X+2  X  2  X  X  0  X  X  2  X X+2  2  0  X X+2  X X+2  2  0  0  2  2 X+2  X X+2 X+2  X X+2  0  0 X+2  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  0  0  2  2  2  2  0  2  2  2  0  2  2  0
 0  0  0  0  0  2  0  2  2  2  2  0  0  0  2  2  0  2  2  2  0  0  0  0  0  2  2  2  0  0  2  2  0  2  0  2  2  0  0  0  2  0  2  2  2  0  0  2  2  0  2  2  2  0  2  0
 0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  2  0  0  2  0  2  2  2  0  0  2  2  0  0  2  0  0  2  0  0  2  2  0  0  2  0  2  0  2  0  0  0  2  0  2  2  0  2  2  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+93x^48+150x^49+297x^50+410x^51+499x^52+740x^53+706x^54+762x^55+969x^56+824x^57+670x^58+714x^59+522x^60+292x^61+199x^62+138x^63+70x^64+34x^65+39x^66+20x^67+19x^68+8x^69+6x^70+4x^71+3x^72+2x^74+1x^78

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 3.72 seconds.