The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+46x^45+166x^46+442x^47+677x^48+938x^49+1507x^50+1936x^51+2450x^52+3098x^53+3413x^54+3490x^55+3419x^56+3066x^57+2479x^58+2036x^59+1413x^60+886x^61+633x^62+306x^63+147x^64+90x^65+58x^66+44x^67+21x^68+2x^69+2x^71+2x^73

The gray image is a linear code over GF(2) with n=220, k=15 and d=90.
This code was found by Heurico 1.16 in 36 seconds.