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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+69x^46+80x^47+166x^48+228x^49+312x^50+304x^51+484x^52+672x^53+619x^54+780x^55+799x^56+774x^57+717x^58+674x^59+441x^60+302x^61+237x^62+170x^63+119x^64+62x^65+66x^66+38x^67+34x^68+10x^69+25x^70+2x^71+3x^72+1x^74+1x^76+2x^78

The gray image is a code over GF(2) with n=224, k=13 and d=92.
This code was found by Heurico 1.16 in 4.65 seconds.