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  X X^2 X^2 X^2 X^2  X  0  X  X  1 X^2  1  0  1  1  1  X  0  1  X  1  X
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  X  X  0  0  0 X^2 X^2+X X^2+X X^2  X X^2+X X^2+X  0  0 X^2+X  X  0  X X^2  X  X  X  X  X  X X^2+X X^2  X X^2+X  0  X  0 X^2 X^2 X^2  X X^2+X X^2 X^2 X^2  X X^2+X
 0  0  X  0  X  X X^2+X  0  0  0  X  X  X  0 X^2 X^2+X  X  0 X^2 X^2  0  0 X^2 X^2+X  X X^2+X X^2 X^2+X  0 X^2+X  X X^2+X  X  0  X  X X^2+X X^2  0 X^2  X X^2  X  0 X^2  X  0 X^2+X  0  0  X X^2+X  0  X  X
 0  0  0  X  X  0 X^2+X  X X^2  X X^2  0  X X^2 X^2+X  X X^2 X^2  X X^2+X X^2  X  X  0 X^2+X X^2+X  0 X^2+X  0  0  0 X^2+X X^2+X X^2+X  0  0 X^2 X^2+X  0  X  0 X^2+X  0  X X^2  0 X^2 X^2  X X^2 X^2+X X^2+X  X  X X^2+X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  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 X^2  0  0  0 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  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 46.

Homogenous weight enumerator: w(x)=1x^0+183x^46+20x^47+375x^48+60x^49+603x^50+236x^51+861x^52+444x^53+1127x^54+500x^55+1099x^56+468x^57+771x^58+260x^59+546x^60+52x^61+301x^62+8x^63+169x^64+81x^66+17x^68+5x^70+3x^72+1x^74+1x^80

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 50.6 seconds.