The generator matrix

 1  0  0  1  1  1 X+2  1  1  1  1 X+2 X+2  0  2  X  1  2  1  1  0  1  1  1  X  1  1  1  2  2  1  1 X+2  1  2 X+2  2  1  2 X+2  2  1  X  1 X+2  2  1  1  1 X+2  1 X+2  1  1 X+2  1
 0  1  0  0  1 X+3  1  2  0  1 X+1  X  1  1  X  1 X+1  1  0  1  2 X+2  0 X+1  1  2  X X+1  1  1 X+2  1  1  1  1  1  X X+3  2  2  1 X+2  0  1  1  2 X+1 X+3  X  1  X  0  0  X  1  0
 0  0  1  1  1  0  1 X+2 X+1 X+1 X+2  1  X X+1  1 X+1 X+3  2 X+3  0  1  0  3 X+2 X+1  0 X+2  2 X+2  3  1  0  0  3 X+3  X  1  1  1  1 X+1 X+1  1 X+1 X+2  1 X+3  2  2 X+3  0  1 X+2  3  2 X+2
 0  0  0  X  0 X+2 X+2 X+2  2  X  2  X X+2  2  0  X X+2 X+2  X  0  X  0  2  X  2 X+2  2  0  0 X+2  X X+2 X+2 X+2  0  0  X  2  0  0  X  2 X+2  0  X X+2 X+2 X+2  2 X+2 X+2  0 X+2  0 X+2  0
 0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  0  2  2  2  2  2  2  2  0  2  0  2  2  2  2  0  0  0  0  2  0
 0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  0  2  0  0  0  2  0  0  2  2  2  2  2  2  0  2  0  2  2  2  2  0  0  2  0  2  2  0  2  2  0  0  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  2  2  2  0  2  2  0  0  2  0  2  2  2  2  2  0  2  0  0  2  0  2  0  2  2  0  2  0  0  0  2  2  2  2  2  0  2  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+214x^48+236x^49+746x^50+728x^51+1233x^52+1112x^53+1610x^54+1492x^55+1780x^56+1520x^57+1562x^58+1172x^59+1154x^60+680x^61+546x^62+188x^63+245x^64+36x^65+68x^66+4x^67+37x^68+12x^70+8x^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 11.3 seconds.