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  0 X^2  0  0  X  1  0  1  1  X  0  X  X  X  X  1  X  1 X^2  X  0  1  1  X
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2 X^2  0  X X^2 X^2+X  X  0 X^2 X^2  X  0  X X^2+X X^2 X^2+X  0 X^2  X  X X^2 X^2  0  0  X  0  X  X X^2+X X^2+X X^2+X  0  X X^2  0  X  X  X X^2+X X^2 X^2
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0  0  X X^2+X X^2+X X^2+X  0 X^2  X X^2+X X^2+X X^2+X  X X^2 X^2+X  X X^2+X  0  0  X X^2+X X^2+X X^2  0  X  X X^2 X^2  X  0  X X^2+X  0  X X^2+X X^2 X^2 X^2 X^2 X^2  0  X X^2+X
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  0  X X^2+X  0  0 X^2+X  X X^2  X  0 X^2 X^2  0  X  X  0  X  0 X^2  0 X^2  X  0 X^2+X  X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2  0 X^2 X^2+X  0  0 X^2+X X^2+X X^2+X X^2
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2+X  0  X X^2+X X^2 X^2  0 X^2+X  X  0  0  X X^2+X  0 X^2 X^2+X X^2  0  0  X  0  X X^2+X X^2+X X^2  0 X^2 X^2+X X^2+X X^2+X  X X^2 X^2+X  X  0 X^2+X X^2 X^2 X^2+X X^2 X^2+X
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  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+189x^46+4x^47+409x^48+72x^49+614x^50+228x^51+853x^52+448x^53+1066x^54+580x^55+1065x^56+424x^57+790x^58+188x^59+550x^60+80x^61+326x^62+24x^63+169x^64+79x^66+24x^68+7x^70+1x^74+1x^76

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 4.68 seconds.