The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+150x^49+299x^50+450x^51+642x^52+784x^53+772x^54+750x^55+784x^56+718x^57+723x^58+656x^59+521x^60+336x^61+240x^62+158x^63+91x^64+66x^65+12x^66+18x^67+7x^68+8x^69+2x^70+2x^72+2x^73

The gray image is a code over GF(2) with n=224, k=13 and d=98.
This code was found by Heurico 1.16 in 3.46 seconds.