The generator matrix

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

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+614x^53+761x^54+708x^55+516x^56+496x^57+306x^58+260x^59+152x^60+154x^61+50x^62+72x^63+3x^64+2x^66+1x^70

The gray image is a linear code over GF(2) with n=448, k=12 and d=212.
This code was found by Heurico 1.16 in 104 seconds.