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  X  X X^2  X  1  1  X  1  0  0  1  1  1 X^2  1  0  1  X X^2  X  1 X^2  X  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X X^2+X X^2+X X^2  0  0 X^2+X X^2 X^2  0 X^2+X  X  X X^2  0  0 X^2  X X^2+X X^2  X X^2+X  X  0 X^2  0  0 X^2  X  0 X^2 X^2+X  X  X  X  X  X  X X^2+X
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X X^2  0 X^2+X X^2+X X^2 X^2+X  X X^2 X^2  0 X^2  X  X  X  0  X  X X^2+X  0  0 X^2+X X^2  0 X^2+X X^2  X  X X^2+X  X X^2+X X^2 X^2+X X^2+X X^2+X X^2  0 X^2  X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2+X  0  X X^2  X  X X^2  0  X  0 X^2+X X^2+X  X X^2+X X^2+X  X  0 X^2 X^2  X  X X^2  X X^2+X  X  0 X^2+X X^2 X^2 X^2+X X^2+X  0  0 X^2  0 X^2+X  0  X
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  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+86x^47+163x^48+116x^49+142x^50+254x^51+388x^52+368x^53+310x^54+438x^55+469x^56+378x^57+253x^58+198x^59+194x^60+114x^61+50x^62+44x^63+46x^64+42x^65+11x^66+4x^67+18x^68+6x^69+1x^72+1x^74+1x^82

The gray image is a linear code over GF(2) with n=220, k=12 and d=94.
This code was found by Heurico 1.16 in 78.8 seconds.