The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  X  1  0  1 X^2+X  1  1 X^2+X X^2  X  1  1  1 X^2+X  1  1 X^2+X  X  1  1  1  1  X X^2  1  1  1  1 X^2+X  0  1  1  1  1  X  1  0 X^2  1 X^2+X  X  1  1  X  1
 0  1  0  0  1  1  1 X^2  0  X X^2+X  1  1 X^2+X+1  1 X^2+X+1  X  1  1  1 X^2+X X+1 X^2+X+1  0 X^2 X^2+X  1  1  1 X^2+X+1  X  X  1 X^2+X X^2+X X^2+X+1  X X^2+1  X  1  0  1 X+1  X  1 X^2+X X^2  0  1 X^2  0 X^2 X^2  X  0
 0  0  1 X+1 X^2+X+1  0 X+1  X X^2+1  1  1  1 X^2+1  X  0  1  1 X+1 X^2+X X^2+1  0  0 X^2+X+1  1 X^2+1  X X^2+X X^2+1  X  1 X+1 X^2+X X^2  1 X+1  X  0 X^2  1 X^2+X+1 X+1 X^2 X+1 X+1 X^2+X X^2+X  1  1 X+1  1  1 X^2  1  1 X^2+X+1
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  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+222x^48+204x^49+606x^50+448x^51+816x^52+544x^53+978x^54+656x^55+1013x^56+616x^57+674x^58+416x^59+496x^60+160x^61+214x^62+16x^63+59x^64+12x^65+16x^66+16x^68+8x^70+1x^72

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 2.82 seconds.