The generator matrix

 1  0  1  1  1 X+2  1  1  0  1 X+2  1  1  2  1  1  X  1  1  1  2  1  1  1  1 X+2  X  1  1  0  X  1  1  1  1 X+2  1  1  1  0  1  1  1  1 X+2  X  1  0  2  1  1 X+2  1 X+2 X+2  1
 0  1  1  0  1  1  X X+3  1 X+2  1 X+3  1  1  0  X  1  3  2 X+1  1 X+2 X+1  1  1  1  1  1  0  1  1  X X+3 X+3  0  1  X X+3  X  1  0  3  2  2  1  2 X+1  1  1  0  0  1  2  1  1 X+3
 0  0  X  0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  2  0  2  2 X+2  X X+2  X X+2  X  X  X  X X+2 X+2 X+2 X+2 X+2 X+2 X+2  0  0 X+2  X X+2 X+2  X X+2  X X+2  X  X  X  2  0 X+2 X+2  0
 0  0  0  X  0  0  X  2  X  2 X+2  X X+2  X  X  2  0  X  0  0 X+2  X  X  X X+2  0 X+2  0 X+2 X+2  X  2  0  2  0  0  2  0  X  X  X  X  2  2  0 X+2  X  X  2  2  2  2  0  X  2  2
 0  0  0  0  X  0  0  X  X  2 X+2  2  2  2 X+2 X+2  X X+2  X  2  0 X+2  0  0  X  X  0 X+2  0 X+2  0  2  2  X X+2  2 X+2  0  X  0  2  2 X+2  2  0  X  X  X  2  0  0  X  X X+2  2 X+2
 0  0  0  0  0  2  2  2  2  2  0  2  0  2  0  2  0  2  0  2  0  0  2  0  0  0  0  2  2  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  0  0  2  2  2  2  0  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+114x^48+72x^49+370x^50+296x^51+775x^52+480x^53+910x^54+672x^55+961x^56+656x^57+884x^58+584x^59+554x^60+256x^61+300x^62+48x^63+152x^64+8x^65+60x^66+30x^68+2x^70+4x^72+2x^74+1x^76

The gray image is a code over GF(2) with n=224, k=13 and d=96.
This code was found by Heurico 1.16 in 3.31 seconds.