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  X  1  0  1  1  X  1  1  1  0  X  1  2  X  0  1  1  X  1
 0  X  0  X  0  0  X X+2  2  2  X X+2 X+2 X+2  2  2  0  X  2  X  X  2  0  X X+2  X  0  0  0  X  0 X+2  0  2  2  0  X  X  0  X  2  X X+2  X  0  2  2  0 X+2  0 X+2  X  2  0  X  2
 0  0  X  X  0 X+2  X  2  0  X  X  0  2  X  2 X+2  0 X+2 X+2  2  2 X+2  0 X+2  0  0  0  2  X  X  X  X  0  X  2 X+2  X X+2 X+2  0  0  2  0  2  X X+2  X  2  0  2  2  2  0  X X+2  X
 0  0  0  2  0  0  2  0  0  0  0  2  2  0  2  2  2  0  2  0  2  2  2  2  0  2  0  2  2  2  0  0  0  0  0  0  0  2  2  2  2  0  0  0  2  0  2  0  2  0  2  0  2  2  2  2
 0  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  2  0  0  2  0  0  0  2  2  2  0  0  2  2  2  2  2  0  0  2  0  2  2  2  0  2  0  0  0  2  0  0  2  0  0  2  0  0  2  2
 0  0  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2  2  0  2  2  2  0  0  0  2  2  2  0  2  0  2  2  0  0  2  2  2  0  0  2  0  0  2  0  0  0  2  2  0  0  2  0  2  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+20x^50+62x^51+62x^52+118x^53+85x^54+156x^55+127x^56+92x^57+115x^58+40x^59+49x^60+6x^61+26x^62+22x^63+16x^64+8x^65+9x^66+6x^67+1x^68+2x^71+1x^94

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 0.154 seconds.