The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+90x^47+380x^48+676x^49+803x^50+1122x^51+1385x^52+1434x^53+1569x^54+1630x^55+1600x^56+1428x^57+1206x^58+1100x^59+885x^60+510x^61+269x^62+128x^63+65x^64+60x^65+21x^66+8x^67+4x^68+4x^69+4x^70+2x^75

The gray image is a linear code over GF(2) with n=220, k=14 and d=94.
This code was found by Heurico 1.13 in 3.14 seconds.