The generator matrix

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

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+53x^50+89x^52+64x^53+97x^54+128x^55+98x^56+320x^57+51x^58+43x^60+35x^62+24x^64+20x^66+1x^104

The gray image is a code over GF(2) with n=224, k=10 and d=100.
This code was found by Heurico 1.16 in 0.167 seconds.