The generator matrix

 1  0  1  1  1  X  1  1 X^3+X^2+X  1  1 X^2+X X^3+X^2+X X^2  1  1 X^2  1  1  1  1  0  1  1  1  X  1  1  1  1  X  1 X^3  1  1  1 X^2  0 X^3+X^2 X^3+X X^3+X^2+X  1  1  1  1  1  1  1 X^3+X^2  1  1  1  1 X^2+X  1  1
 0  1  1 X^2 X+1  1  X X^3+1  1 X^3+X X^2+X+1  1  1  1 X^2 X^3+X^2+1  1 X^3 X^2+1 X^3+X^2+X+1  X  1 X^3+X X^2+1 X^2+1  1 X^3+X+1 X+1 X^3 X^2+X+1  1 X^3+X^2+X  1 X^3+X^2  1 X^3+X^2+X  1  1  1  1  1 X^3 X^2  1 X^2+X X^3+X^2+X+1 X^2+X X+1 X^2 X^3+X+1 X+1 X^2+1 X^3+X^2  1 X^2+X+1 X^3
 0  0  X X^3+X X^3 X^3+X X^3+X X^3 X^3+X^2+X  0  X  0 X^3+X^2 X^2 X^3+X^2+X X^3+X^2 X^3+X X^3+X^2 X^3+X^2+X X^3 X^2 X^2+X X^2+X  0 X^3+X  0  X X^2 X^3+X X^2+X X^3+X^2+X  X X^3+X^2 X^2 X^2 X^2 X^3+X^2+X  X X^3 X^3+X^2 X^3+X X^3+X^2+X X^3 X^2+X  0 X^2 X^3+X^2+X X^2+X  X X^2+X X^3+X^2+X X^3  X X^2 X^3+X^2 X^3+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+296x^53+436x^54+266x^55+188x^56+236x^57+310x^58+206x^59+34x^60+32x^61+20x^62+20x^63+1x^70+1x^74+1x^76

The gray image is a linear code over GF(2) with n=448, k=11 and d=212.
This code was found by Heurico 1.16 in 0.671 seconds.