The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+40x^53+6x^54+44x^55+14x^56+4x^57+8x^58+4x^59+2x^62+1x^64+4x^69

The gray image is a linear code over GF(2) with n=220, k=7 and d=106.
This code was found by Heurico 1.16 in 0.605 seconds.