The generator matrix

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

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+173x^48+8x^49+40x^50+80x^51+190x^52+248x^53+88x^54+352x^55+198x^56+248x^57+88x^58+80x^59+140x^60+8x^61+40x^62+54x^64+6x^68+5x^72+1x^88

The gray image is a linear code over GF(2) with n=220, k=11 and d=96.
This code was found by Heurico 1.16 in 53.9 seconds.