The generator matrix

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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+39x^46+126x^47+406x^48+420x^49+563x^50+582x^51+816x^52+718x^53+1006x^54+690x^55+825x^56+520x^57+559x^58+342x^59+237x^60+120x^61+124x^62+48x^63+12x^64+12x^65+10x^66+4x^67+7x^68+2x^69+3x^70

The gray image is a linear code over GF(2) with n=216, k=13 and d=92.
This code was found by Heurico 1.16 in 2.66 seconds.