The generator matrix

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

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+92x^51+131x^52+194x^53+147x^54+126x^55+61x^56+54x^57+36x^58+46x^59+45x^60+32x^61+23x^62+24x^63+2x^64+8x^65+2x^66

The gray image is a linear code over GF(2) with n=220, k=10 and d=102.
This code was found by Heurico 1.11 in 0.062 seconds.