The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+272x^54+58x^56+128x^58+48x^62+3x^64+2x^72

The gray image is a linear code over GF(2) with n=224, k=9 and d=108.
This code was found by Heurico 1.16 in 17.1 seconds.