The generator matrix

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

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+6x^54+44x^55+7x^56+2x^59+1x^62+2x^67+1x^70

The gray image is a linear code over GF(2) with n=220, k=6 and d=108.
This code was found by Heurico 1.16 in 0.0794 seconds.