The generator matrix

 1  0  1  1  1  0  1  1  2  1  1  0  1  1 X+2 X+2  1  1  1  1  1  X  X  1  0  X  1  0  1  1  1  1 X+2  1 X+2  0  1  1  1  0  1  1  2  1  2  1  1  1  2  X  X X+2  1  X  X  1
 0  1  1  0  1  1 X+1  2  1 X+1  0  1  X  3  1  1  X X+3 X+2  1 X+1  1  1 X+2  1  1 X+1  1  0  3  0  3  1  3  1  1 X+2 X+3  X  1  0  1  1 X+2  1 X+3  0  1  1 X+2  X  1 X+2  2  1  0
 0  0  X  0  0  0  0  X  X  X  X  X X+2 X+2  X  2  0  2 X+2 X+2  0  2  X  0  0  0  2  X  0 X+2  0  2  X  X  2  X  X  0  2  X  X X+2  0  X  2  2  X  X  2 X+2  2 X+2  0  2  0  0
 0  0  0  X  0 X+2  X  X X+2  X  0  2  X X+2  2  2 X+2  2  0  2 X+2 X+2 X+2  0  0  0  0  2  X  X X+2 X+2  X  0  0  X  0  0  0 X+2  2  X  X  X  2  X  X X+2 X+2  2 X+2  0  X X+2 X+2  X
 0  0  0  0  X  0  X X+2 X+2  2  X X+2  X  2  X  2  2 X+2 X+2  2  X  0  X  2  0  X  0  0  X X+2 X+2  2  2 X+2 X+2  X  2  0  2  X  2  2  X  0 X+2  0  0  X  X  2  2  0  0  0  0 X+2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  2  2  2  0  0  2  0  2  0  2  2  0  0  2  0  0  2  0  0  0  2  0  2  2  0  2  2  2  2  0  2
 0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  0  2  2  0  0  0  0  2  2  0  2  2  2  2  0  0  0  0  2  2  0  2  0  2  0  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+50x^46+106x^47+187x^48+358x^49+547x^50+700x^51+939x^52+1304x^53+1534x^54+1620x^55+1783x^56+1740x^57+1451x^58+1226x^59+916x^60+694x^61+498x^62+276x^63+178x^64+116x^65+73x^66+34x^67+25x^68+10x^69+6x^70+6x^71+3x^72+2x^73+1x^74

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 12.4 seconds.