The generator matrix

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

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+120x^46+372x^47+754x^48+1000x^49+1693x^50+2232x^51+2363x^52+2846x^53+3205x^54+3496x^55+3251x^56+3012x^57+2653x^58+2032x^59+1528x^60+992x^61+592x^62+292x^63+161x^64+84x^65+53x^66+24x^67+5x^68+2x^69+3x^70+1x^72+1x^74

The gray image is a linear code over GF(2) with n=220, k=15 and d=92.
This code was found by Heurico 1.16 in 33.3 seconds.