The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^3+X^2  1 X^2+X  1  1  1 X^3+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^3 X^3+X^2  1  1  1  1 X^2 X^2+X X^3+X^2+X  X  X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^3+X^2+X+1  1 X^2+1  1 X^3+X^2 X^3+X X^3+1  1  0 X^2+X X+1 X^3+1 X^3+X^2 X^3+X^2+X+1 X^2+1 X^3+X^2+X X^3+X X^3 X^2  X X^3+X+1 X^3+X^2+1 X^2+X+1  1  0 X^3+X^2+X X^3 X^3+X^2+X  1  1  1 X^3  X  X X^3  1  1  1 X^3+X^2 X^3+X^2
 0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0
 0  0  0 X^3 X^3 X^3 X^3  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  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  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 54.

Homogenous weight enumerator: w(x)=1x^0+384x^54+266x^56+360x^58+3x^60+8x^62+1x^76+1x^80

The gray image is a linear code over GF(2) with n=448, k=10 and d=216.
This code was found by Heurico 1.16 in 16.6 seconds.