The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+50x^54+32x^55+29x^56+10x^58+1x^60+4x^62+1x^68

The gray image is a linear code over GF(2) with n=220, k=7 and d=108.
This code was found by Heurico 1.16 in 0.06 seconds.