The generator matrix

 1  0  0  0  0  1  1  1  0 X^2  1  1  1  0  0 X^2+X  1  1 X^2  X  X  X  X  1  1  1  0  1  X  1  1 X^2  1  0  X  1  X  1 X^2  1  1  0 X^2+X  1  1  1  1  1 X^2+X  1 X^2+X X^2 X^2+X  0  0
 0  1  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  1  1  1 X^2+1  1  1 X^2+X+1  1 X^2+X+1 X+1  1  X  1  X  1  1  X  X X^2+X+1 X^2+1 X^2+X  1 X^2+X X^2+1 X^2+X X^2+1 X^2+X  X  X  1  X  1  1  1
 0  0  1  0  0  0  1  1  1  1 X^2 X^2+X+1 X+1  1  X  0  X X^2+1  1  1  1  1 X^2+1 X+1  X X^2+1 X^2+X X^2  1 X^2+X X^2+X X^2+X+1  0 X^2  1 X^2 X+1 X^2  0 X^2+1  X  1  X X+1 X^2 X^2 X^2 X^2+1 X^2+X X^2+X X^2  1 X+1 X+1 X+1
 0  0  0  1  0  1  1 X^2 X^2+1 X^2+1  X  1  X X^2+X  1  0 X+1  X X^2+X+1 X^2+1 X^2  0 X^2+1 X^2+X X^2+1 X^2+X+1 X^2+1 X+1 X^2  0  0 X^2+X+1 X+1  X  X X^2+X+1 X^2 X^2  1  1  0 X^2+1 X+1  X X+1 X^2+X X^2 X^2+1  1 X^2+1 X^2+1 X^2+X+1 X^2+X+1  1 X^2
 0  0  0  0  1  1 X^2 X^2+1 X^2+1  X X^2+X+1 X^2+X+1  0 X+1 X+1  1 X^2+X  1 X^2+X+1 X^2 X+1 X^2 X^2+X  0 X^2  0 X^2+X X+1 X+1  X X^2+X+1 X^2 X^2+1  1  X X^2+X+1 X^2+X+1  0  0 X+1  X  1 X^2  X  0  X  1  0  1  0 X^2+X+1  X X^2+1 X^2+1 X^2+X
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 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+351x^46+796x^47+1467x^48+2256x^49+3066x^50+3936x^51+4981x^52+5940x^53+6276x^54+6796x^55+6780x^56+6016x^57+5368x^58+4280x^59+2758x^60+1972x^61+1243x^62+624x^63+364x^64+136x^65+70x^66+16x^67+27x^68+10x^70+4x^72+2x^76

The gray image is a linear code over GF(2) with n=220, k=16 and d=92.
This code was found by Heurico 1.13 in 45.3 seconds.