The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+28x^52+68x^54+64x^55+69x^56+20x^58+5x^60+1x^108

The gray image is a linear code over GF(2) with n=220, k=8 and d=104.
This code was found by Heurico 1.16 in 0.0843 seconds.