The generator matrix

 1  0  0  0  1  1  1  1  2  1  X  1 X+2  1  2  X  X  2  1  0  1  2  1  1  0  1  X  1  2 X+2 X+2  1 X+2  1  1  1  1  1  1  X  2  1  1  2  1  0  1 X+2  0  2  0  X  1  1  1  1
 0  1  0  0  0  1  2  3  1 X+2  0 X+1  1  1  1  1  1  2  0  0 X+2 X+2  3 X+3  1 X+2  1  2  1  2  0  3  1 X+2 X+3  1  X X+1  0  1  0  1  1  1  X  1 X+2 X+2 X+2  1  2  1  2  0  3  2
 0  0  1  0  0  1  3  2  3  1  1  3  X X+2  1  X  2  1 X+3  1  1  0 X+3  X  2 X+3 X+2 X+2  3  2  1 X+2  1 X+2  2  X  3 X+3  X X+1  X X+3 X+1  3 X+3 X+3  0  0  1 X+3  1 X+2  3 X+1  X X+3
 0  0  0  1  1  2  1  3  3  0 X+3  3 X+3 X+2  X  1  0  X  3  1 X+2  1 X+3 X+2  X  1  3  3  3  1 X+3  3  2  2  2 X+1  X  1  1  2  1  1 X+2  2  2 X+3  X  1  2 X+3 X+2 X+1 X+1  X  0 X+1
 0  0  0  0  X  0  0  0  0 X+2  X  X  X X+2 X+2  X  2  2  2 X+2  X  2  X  2  X X+2  2  0  X  X  0 X+2 X+2  X  0  2  2  2  X X+2  2  X X+2  2 X+2  2  2  2  0  X  0  2  2  2  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+105x^48+424x^49+524x^50+932x^51+1112x^52+1452x^53+1432x^54+1540x^55+1493x^56+1660x^57+1406x^58+1394x^59+874x^60+854x^61+494x^62+350x^63+181x^64+72x^65+43x^66+18x^67+8x^68+2x^69+4x^70+6x^71+2x^72+1x^74

The gray image is a code over GF(2) with n=224, k=14 and d=96.
This code was found by Heurico 1.13 in 3.64 seconds.