The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  X  1  2  1  1  1  1  0  1  1 X+2  1  X  1  1  1  1  1 X+2  0  2  1  1  1  2  1  0  1  1  0 X+2  1  0  1  1  1  1  1  1  0  1  1  X  X  0  1
 0  1  1 X+2 X+3  1  0 X+1  1  X  1  3  1  0 X+3  2 X+3  1  X  1  1 X+2  1  3 X+1  0 X+3 X+2  1  1  1  3 X+3  X  1  1  1  X X+3  1  1 X+3  1  0  1  2  2 X+2  2  X X+2  0  1 X+2  1  2
 0  0  X  0 X+2  0 X+2  0 X+2 X+2  X  2  X  2  X  X  2  2  X  X  0  0 X+2  0  2  0  X  0  0  2 X+2  0 X+2  X X+2  2  X X+2  X  0  2  X  0  2 X+2  X  0  2  0  X X+2  0  2  X X+2 X+2
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  2  0  2  0  0  0  2  2  0  0  2  0  2  2  2  0  0  2  0  2  0  0  0  0  2  2  2  0  2  2  2  0  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  2  2  2  0  2  2  0  0  0  2  0  0  2  2  0  0  2  2  0  2  2  0  2  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  2  0  0  0  2  0  2  2  0  2  0  0  0  0  0  2  2  0  2  0  2  0  2  2  0  0  2  2  2  2  0  0  2  0  2  2  2  0
 0  0  0  0  0  0  2  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  2  0  0  0  0  0  2  2  0  2  0  0  2  0  2  0  2  0  0  0  2  0  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  0  2  2  2  2  2  2  2  2  0  0  0  0  0  2  2  0  0  2  2  0  0  2  0  2  2  0  2  2  2  2  2  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  0  2  0  0  0  0  0  2  2  2  2  0  2  2  2  2  0  2  0  2  0  0  2  0  2  0  2  0  2  2  0  2  0  2  0  0  0  0  2  0  0  0  2  2  0

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+105x^46+375x^48+96x^49+725x^50+328x^51+1554x^52+632x^53+2120x^54+968x^55+2600x^56+1016x^57+2144x^58+664x^59+1483x^60+296x^61+673x^62+88x^63+342x^64+8x^65+101x^66+32x^68+14x^70+10x^72+6x^74+3x^76

The gray image is a code over GF(2) with n=224, k=14 and d=92.
This code was found by Heurico 1.16 in 44 seconds.