The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+70x^49+232x^50+460x^51+437x^52+492x^53+369x^54+336x^55+328x^56+348x^57+279x^58+244x^59+161x^60+142x^61+59x^62+64x^63+41x^64+18x^65+13x^66+2x^69

The gray image is a linear code over GF(2) with n=220, k=12 and d=98.
This code was found by Heurico 1.11 in 0.235 seconds.