The generator matrix

 1  0  0  1  1  1  2  0  0  2  1  1  1  1  1 X+2  1  X  X  1 X+2  1  0  1  1  1  1  1  0  1  1  0  X X+2  1  1  2  1  1  1  0 X+2 X+2  1  1  2  1  X X+2 X+2  X  0  0  1 X+2  2
 0  1  0  0  1 X+1  1  1  1  X  X X+3 X+2  3  2  1  1 X+2  0  X  1  3  1  3 X+3 X+2  2  2  1  1  1  1  1  1  X  0  1  X X+2 X+2  0  2  1  3  2  1  0  1  1  X  1 X+2  1 X+1  2  X
 0  0  1  1  1  0 X+1  1 X+2  1  X X+1  1  0 X+2  2 X+3  1  1 X+1  1  3  0 X+2  0  2 X+2 X+3 X+1  3  X  X X+1  2  1  1  0 X+3 X+2  X  1  1  1  0 X+2  1 X+3 X+3  0  1 X+1  1 X+1 X+3  1  1
 0  0  0  X X+2  0  X  X  0  0  2  X  X  0  2  0 X+2  2  2 X+2 X+2  X  2  2  0  2 X+2  2  0  0 X+2  X  0 X+2  0  0  X X+2 X+2  0  2  X  2 X+2  X X+2  2  0  X X+2 X+2 X+2  2  0  0  0
 0  0  0  0  2  0  0  2  2  2  2  0  0  2  0  2  0  2  0  2  0  2  0  0  2  0  2  2  2  0  0  2  2  0  0  2  2  2  0  2  0  2  0  2  0  0  0  0  2  0  2  2  2  0  2  0
 0  0  0  0  0  2  2  0  2  2  2  2  2  2  2  0  0  0  2  0  0  2  2  0  0  2  2  0  0  0  2  2  2  2  2  0  0  2  2  0  2  2  0  2  0  0  0  2  0  0  0  2  2  2  0  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+186x^49+196x^50+646x^51+497x^52+810x^53+630x^54+948x^55+555x^56+1006x^57+568x^58+768x^59+339x^60+454x^61+206x^62+244x^63+36x^64+32x^65+32x^66+10x^67+12x^68+8x^69+8x^71

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 3.68 seconds.