The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  0 X+2  1  1  1  X  1  1  2  1  2  1  1  2  1  1  1 X+2  1  1 X+2  1  1  2  1  1  1  1  1  X  1  X  2  2  1  0  1  X  1  1  1  X  1  1  1  0
 0  1  1  0 X+3  1  0 X+1  1  2  1  1  3  X X+3  1 X+2  3  1 X+2  1  1  3  1  0  X X+3  1  1 X+2  1  3 X+2  1 X+3  2  2 X+3 X+2  1  X  1  0  1  X  2  2  1  2  3  2  0 X+3 X+1  0  1
 0  0  X  0 X+2  0  X  0  X  X X+2  2  2  X  0  X X+2 X+2  0  2 X+2  2 X+2  X  0  0 X+2  X  0 X+2  0  2  X  2 X+2 X+2  0 X+2  X X+2 X+2 X+2  0 X+2  X  X  X X+2 X+2  X  2  0  2 X+2  0  X
 0  0  0  X  0  0  X  0  0  2  X  X  0  2  X  2  X X+2 X+2  0  2  X  X  X  2  X  X  X X+2  X  0 X+2  2 X+2  0  0  X  0  2  X  X  0  X  2  X  X  2  X X+2  2  X X+2  0  X  X  X
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  0  2  2  0  2  0  0  2  2  2  0  2  2  2  0  0  0  2  2  2  0  0  2  2  0  0  2  2  2  2  0  0  2  0  2  0  2  0  0
 0  0  0  0  0  2  0  0  2  0  2  2  2  0  2  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  0  2  2  2  0  2  0  0  0  2  2  0  2  2  2  0  0  2  0  0  2  0  2
 0  0  0  0  0  0  2  0  2  2  2  0  0  2  0  0  0  0  2  0  0  2  2  2  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  0  0  2  0  2  0  2  0  2  0  2  0  0  2  2
 0  0  0  0  0  0  0  2  0  0  0  0  2  0  2  2  2  0  2  0  2  0  2  0  0  0  2  2  2  0  0  2  2  0  2  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  0  0  0  0  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+53x^46+116x^47+209x^48+300x^49+545x^50+680x^51+998x^52+1362x^53+1419x^54+1674x^55+1749x^56+1690x^57+1517x^58+1274x^59+918x^60+654x^61+489x^62+298x^63+188x^64+82x^65+62x^66+54x^67+28x^68+8x^69+7x^70+5x^72+3x^74+1x^82

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 12.1 seconds.