The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+64x^51+63x^52+184x^53+54x^54+172x^55+50x^56+116x^57+30x^58+136x^59+34x^60+80x^61+10x^62+12x^63+8x^64+4x^65+2x^66+1x^68+1x^72+1x^76+1x^84

The gray image is a linear code over GF(2) with n=224, k=10 and d=102.
This code was found by Heurico 1.16 in 0.119 seconds.