The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1  1 X^2  0  1  1  X X^2+X  1  1  1  0  0  X  1  1  0  1 X^2+X  1  X  X  1  1  X X^2 X^2  0  1  1  1  0  X X^2+X X^2  X  X  1  1  1  1  1  1  1
 0  1  0  0  0  0  0 X^2 X^2  1  1  1  1  1  1  1  0 X^2  0 X^2+1 X^2 X^2+X X^2+X  1  1  1 X^2+X X^2+X X^2+1  X X^2+X  1 X^2+X X^2+X+1 X^2+X+1  1  X  1  X X^2  0 X+1  1  1  0  X  1  0  1 X^2+X+1 X^2  X  X X+1  0
 0  0  1  0  0 X^2  1 X^2+1  1  0  1 X+1 X^2+X+1 X^2+X+1 X^2 X^2+X  X  X  1  0 X^2+X+1 X^2+X+1  1  1 X^2 X^2+X  0  X X^2+1  1  1 X^2+X  1 X^2+X+1 X^2  1  1 X^2+1  1  X  1  0  X X^2  1  0  X  1 X^2+X+1  0 X+1  1 X^2+X X^2  0
 0  0  0  1  0 X^2+1  1  0  1 X^2 X^2+1 X+1  X X^2+X X^2+X+1  1 X^2  1  1  1 X^2+X  1 X^2 X+1 X^2+X+1  0 X^2+X+1 X^2+X  1  0 X+1  X X^2+X X^2+X+1  X  0  1  X X^2+X+1 X^2 X^2 X^2+1 X^2+X+1 X^2 X^2+X+1  1  0  1  X  0 X^2+1 X^2+1  1 X^2+X+1 X^2
 0  0  0  0  1  1 X^2  1  1 X^2+1 X^2  1  X X^2+X+1 X^2+1  0 X+1  1  X X^2+X+1 X^2 X^2+1  1 X^2+X+1  0  X  0  1 X^2+X X^2+X+1 X+1 X+1  1 X^2+X  X  0 X+1 X+1  X X^2 X^2+X  X  0 X^2+1 X^2+X X^2 X+1 X^2+X+1  0 X+1  0 X^2  1 X^2 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+76x^46+352x^47+717x^48+1284x^49+1512x^50+2238x^51+2370x^52+2928x^53+3315x^54+3308x^55+3146x^56+3028x^57+2504x^58+2152x^59+1525x^60+1204x^61+503x^62+326x^63+172x^64+48x^65+20x^66+22x^67+3x^68+4x^69+4x^70+2x^71+2x^72+2x^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 1.13 in 10.8 seconds.