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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+26x^46+62x^47+96x^48+182x^49+186x^50+262x^51+295x^52+328x^53+433x^54+428x^55+453x^56+348x^57+295x^58+204x^59+133x^60+128x^61+58x^62+54x^63+32x^64+30x^65+22x^66+14x^67+11x^68+8x^69+3x^70+1x^72+1x^74+1x^76+1x^80

The gray image is a linear code over GF(2) with n=220, k=12 and d=92.
This code was found by Heurico 1.16 in 1.07 seconds.