The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+152x^48+256x^49+570x^50+548x^51+759x^52+616x^53+938x^54+772x^55+824x^56+676x^57+686x^58+444x^59+396x^60+192x^61+174x^62+60x^63+67x^64+20x^65+26x^66+9x^68+4x^70+2x^74

The gray image is a linear code over GF(2) with n=220, k=13 and d=96.
This code was found by Heurico 1.16 in 2.84 seconds.