The generator matrix

 1  0  0  1  1  1  0  1  1  2  2  0  1  1  X X+2  1 X+2  1  1  1  X  1  1  1  0  1  2  1 X+2  1  X  1  1  X  0  2  X  1  1  1  2  X  1  1  1  2 X+2  1  1  2  2 X+2  X  1  1
 0  1  0  0  1  1  1  0  2  X  1  1 X+1  1 X+2  0  3  1  X  1  0  1 X+2 X+1 X+3  1  2  2 X+2  1  0 X+2  3 X+3  0 X+2  1  1 X+3  X  2  1  1  3  0  3  1  1  2  3  X  1  1  1 X+2 X+3
 0  0  1 X+1 X+3  0 X+1 X+2  1  1  X  3 X+1  X  1  1  3 X+3 X+2  X  3  X X+1  2  1  0  X  1  0  3  2  1  3  X  1  1 X+1  2 X+1  1  2  3 X+2 X+1  2 X+1 X+3  0 X+3  1  1  1  3  1  X  X
 0  0  0  2  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  0  2  0  0  2  0  0  0  2  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  0  0  2  2  2  2  0  2  2  2  2  0  0  2  2  2  0  0  0  0  2  0  2  0  2  2  2  0  2  2  2  0  2  0  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  0  2  2  2  2  2  2  0  2  0  2  0  2  0  0  0  0  2  2  0  2  2  2  0  2  2  0  0  0  0  0  2  2  2  2  2  2  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  2  2  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  2  0  2  2  0  0  2  2  0  2  2  0  2  2  2  2  0  0  0  2  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  0  0  2  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+286x^48+232x^49+722x^50+580x^51+1339x^52+928x^53+1740x^54+1352x^55+2150x^56+1328x^57+1824x^58+944x^59+1174x^60+544x^61+636x^62+184x^63+249x^64+40x^65+62x^66+12x^67+39x^68+8x^70+10x^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 91.5 seconds.