The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+59x^44+264x^45+851x^46+1758x^47+2515x^48+3964x^49+5750x^50+8026x^51+9430x^52+12342x^53+12870x^54+14464x^55+13109x^56+12896x^57+10247x^58+8240x^59+5512x^60+3902x^61+2230x^62+1222x^63+681x^64+402x^65+167x^66+78x^67+51x^68+20x^69+13x^70+4x^71+2x^72+2x^73

The gray image is a linear code over GF(2) with n=220, k=17 and d=88.
This code was found by Heurico 1.13 in 160 seconds.