The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+28x^52+40x^53+108x^54+72x^55+87x^56+40x^57+40x^58+24x^59+41x^60+16x^61+12x^62+1x^68+2x^84

The gray image is a code over GF(2) with n=224, k=9 and d=104.
This code was found by Heurico 1.16 in 0.0771 seconds.