The generator matrix

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

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+94x^46+380x^47+729x^48+1160x^49+1594x^50+2062x^51+2524x^52+2898x^53+3226x^54+3366x^55+3289x^56+3072x^57+2688x^58+1968x^59+1410x^60+1036x^61+614x^62+332x^63+164x^64+88x^65+38x^66+18x^67+10x^68+2x^69+2x^70+2x^71+1x^72

The gray image is a linear code over GF(2) with n=220, k=15 and d=92.
This code was found by Heurico 1.16 in 32.5 seconds.