The generator matrix

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

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+66x^46+394x^47+838x^48+1490x^49+2048x^50+3126x^51+3707x^52+5492x^53+5455x^54+6726x^55+6447x^56+7026x^57+5587x^58+5836x^59+3771x^60+3018x^61+1903x^62+1248x^63+676x^64+348x^65+161x^66+76x^67+46x^68+34x^69+12x^70+2x^72+2x^75

The gray image is a code over GF(2) with n=224, k=16 and d=92.
This code was found by Heurico 1.13 in 49.5 seconds.