The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  1  0  0  1  1 X+2  1  1  1  X  1  2 X+2  1  1  0  1  1  1  1  1  1  X  X  0  0  1  1  2  1  0 X+2  1  1  1  X  1 X+2  1  1 X+2  1  1
 0  1  1  0 X+3  1 X+1 X+2  1  2  1  3  X X+1  1  1  0  3  1  X X+1  X  1  1  1  1 X+3  0  1 X+1  2 X+1  0 X+3  3  1  1  1  1  3  0  1  3  X  1  X  3  2  1 X+2  1 X+2 X+2  1  X  0
 0  0  X  0 X+2  0  2  2  X X+2 X+2  2  X  X  X  0  X  2 X+2  2  2 X+2  2 X+2  2  X  2  2  X  X  X  0  0  2 X+2  2  2  2  0 X+2  0  X X+2  X  X  0  0  2  X  X X+2  X X+2  2  2 X+2
 0  0  0  X  0  0  0  2  2  2  2  0  0  X  X  X X+2  X  X X+2  X X+2 X+2 X+2  0  0 X+2  2 X+2  X  0  0 X+2  0  2  2  X X+2  0  2  2  2  X X+2  X  X  X X+2  X  X  0 X+2  X  X  2 X+2
 0  0  0  0  2  0  0  0  2  2  0  0  0  2  2  0  0  2  2  0  0  0  2  0  2  0  2  2  0  2  2  2  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  2  0  2  2  2  2  2  0  2
 0  0  0  0  0  2  2  2  0  2  0  0  2  0  0  0  0  2  2  2  2  2  2  0  0  2  0  2  2  2  0  0  2  2  2  0  2  0  2  2  0  2  2  0  2  0  2  0  0  0  0  0  0  0  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+52x^49+136x^50+244x^51+334x^52+376x^53+388x^54+380x^55+380x^56+398x^57+411x^58+320x^59+251x^60+178x^61+72x^62+60x^63+46x^64+14x^65+9x^66+20x^67+11x^68+6x^69+7x^70+1x^72+1x^78

The gray image is a code over GF(2) with n=224, k=12 and d=98.
This code was found by Heurico 1.16 in 0.785 seconds.