The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+80x^47+174x^48+284x^49+433x^50+544x^51+669x^52+740x^53+776x^54+904x^55+878x^56+698x^57+616x^58+476x^59+331x^60+216x^61+132x^62+90x^63+40x^64+46x^65+27x^66+16x^67+16x^68+2x^71+3x^72

The gray image is a linear code over GF(2) with n=220, k=13 and d=94.
This code was found by Heurico 1.16 in 17.9 seconds.