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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+66x^45+130x^46+182x^47+303x^48+380x^49+484x^50+684x^51+834x^52+1108x^53+1442x^54+1574x^55+1840x^56+1736x^57+1469x^58+1260x^59+823x^60+658x^61+446x^62+318x^63+238x^64+124x^65+102x^66+72x^67+45x^68+24x^69+22x^70+6x^71+10x^72+1x^74+1x^76+1x^84

The gray image is a code over GF(2) with n=224, k=14 and d=90.
This code was found by Heurico 1.16 in 16.8 seconds.