The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+64x^53+96x^54+122x^55+55x^56+48x^57+45x^58+18x^59+14x^60+20x^61+10x^62+16x^63+1x^64+1x^68+1x^78

The gray image is a code over GF(2) with n=224, k=9 and d=106.
This code was found by Heurico 1.13 in 0.046 seconds.