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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+188x^46+395x^48+48x^49+572x^50+244x^51+860x^52+400x^53+1066x^54+636x^55+1159x^56+464x^57+804x^58+204x^59+511x^60+48x^61+338x^62+4x^63+155x^64+68x^66+20x^68+4x^70+2x^72+1x^84

The gray image is a linear code over GF(2) with n=220, k=13 and d=92.
This code was found by Heurico 1.16 in 4.41 seconds.