The generator matrix

 1  0  0  1  1  1  0  1  1  1 X^2+X  1  0 X^2  1  1  1 X^2+X  1  X  X X^2+X X^2+X  1  1  1  1  1 X^2  1  1  0  0  1  1  1  X  1  1  1  1  1  X X^2+X X^2  1  1 X^2  0 X^2  1 X^2 X^2  1  1
 0  1  0  0  1  1  1 X^2 X^2+X+1 X+1  1  X  1 X^2+X X^2+X X^2+X+1 X^2+X  1  1 X^2+X  1  0  1  0  0 X^2+1 X+1 X^2+X  1 X^2+X+1 X^2+X  1 X^2 X^2+1 X+1  0  0 X^2  1 X^2+1 X^2 X^2+X  1  1 X^2  1 X^2+X+1 X^2+X  X  1 X^2+X+1  1  1  1 X^2+X+1
 0  0  1 X+1 X^2+X+1  0 X+1  X X^2+X X^2+X+1 X^2+X+1 X^2+1 X^2+X  1 X^2  1 X+1 X^2  X  1  1  1 X^2+X  X X^2+1 X^2+1  0 X^2+X X^2+X+1  1 X^2+1 X^2+X  1 X^2+X  0 X^2+X+1  1 X^2+1  0  1  1 X^2+1 X^2+1  0  1  0  1  1  1 X^2+X X^2  0 X^2+X X+1 X^2+X
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0
 0  0  0  0 X^2  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 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+142x^49+238x^50+338x^51+465x^52+408x^53+410x^54+374x^55+353x^56+336x^57+303x^58+260x^59+141x^60+128x^61+96x^62+48x^63+30x^64+10x^65+6x^66+2x^67+2x^68+2x^70+2x^71+1x^74

The gray image is a linear code over GF(2) with n=220, k=12 and d=98.
This code was found by Heurico 1.16 in 1.14 seconds.