The generator matrix

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

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+35x^46+64x^47+163x^48+262x^49+466x^50+520x^51+627x^52+806x^53+754x^54+884x^55+836x^56+746x^57+618x^58+496x^59+355x^60+198x^61+148x^62+68x^63+51x^64+32x^65+23x^66+16x^67+14x^68+4x^69+3x^70+1x^72+1x^74

The gray image is a linear code over GF(2) with n=220, k=13 and d=92.
This code was found by Heurico 1.16 in 3.41 seconds.