The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+149x^50+168x^51+466x^52+332x^53+552x^54+344x^55+398x^56+272x^57+426x^58+228x^59+342x^60+92x^61+124x^62+80x^63+60x^64+8x^65+25x^66+12x^67+11x^68+4x^70+1x^72+1x^76

The gray image is a code over GF(2) with n=224, k=12 and d=100.
This code was found by Heurico 1.16 in 0.646 seconds.