The generator matrix

 1  0  0  1  1  1  2  1  1 X+2  1  1  X  0  1  1  X  2  1  1  1  0  X  1  2  1  1  0  1 X+2  1  1 X+2 X+2  1  0 X+2  1  1  2  1  1  0  1  1 X+2  1  1  2  1  1  1  1  1  1  0
 0  1  0  0  1 X+1  1  2  0  0 X+3 X+3  1  1 X+2 X+3  1  1  X X+1  2  X  2  X  1 X+3 X+3  1 X+3 X+2  2  X  1  1  3  1  1  3  0  X  1  X  1 X+3  X  X X+3  2  1  0  1  3 X+3 X+1  X  X
 0  0  1  1  1  0 X+1  X X+3  1  X X+1 X+1  0 X+2  0  3 X+2  X  3 X+3  1  1 X+1  2 X+2 X+3 X+3  1  1 X+1  X X+3  0 X+2 X+3 X+2  0 X+2  1 X+2 X+1  3  X  2  1 X+1  X  1  3 X+1 X+2  1  0  1  1
 0  0  0  X  0  X  0  2 X+2  2  X  2  2 X+2  2  0 X+2  2 X+2 X+2  0  X X+2  0 X+2  0  0  X  X X+2 X+2  0 X+2  0  0  2 X+2 X+2  2  2  0  0 X+2 X+2  2  X  X  X  2 X+2  0  X  X X+2 X+2  0
 0  0  0  0  X  X  X  2  2  2  X X+2  X  X  2  X  X  X  0 X+2  2  2  0  2  0  0  0  0  2  X X+2 X+2  2  2  2  0  0  X  X X+2  0 X+2 X+2  0  2 X+2  2  2  2 X+2  X X+2 X+2  X  2  X
 0  0  0  0  0  2  2  2  2  2  0  2  0  0  2  0  0  0  0  2  2  0  2  0  2  0  2  0  2  2  2  0  0  2  2  2  0  2  0  2  2  2  2  2  2  0  0  2  2  0  0  0  0  0  0  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+240x^48+304x^49+574x^50+812x^51+1165x^52+1232x^53+1530x^54+1652x^55+1424x^56+1848x^57+1314x^58+1340x^59+1094x^60+736x^61+530x^62+220x^63+195x^64+40x^65+72x^66+8x^67+37x^68+12x^70+4x^72

The gray image is a code over GF(2) with n=224, k=14 and d=96.
This code was found by Heurico 1.16 in 11.4 seconds.