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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  X  X  X
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^2  0  0 X^3 X^3 X^3 X^3+X^2  0  0 X^3+X^2  0 X^2 X^3+X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0 X^2 X^2  0 X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3  0 X^3 X^3  0 X^3+X^2  0  0 X^2 X^3 X^3 X^3+X^2 X^3+X^2
 0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3

generates a code of length 56 over Z2[X]/(X^4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+20x^53+42x^54+112x^55+178x^56+104x^57+20x^58+16x^59+12x^60+4x^61+1x^64+2x^78

The gray image is a linear code over GF(2) with n=448, k=9 and d=212.
This code was found by Heurico 1.16 in 0.14 seconds.