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  X  0  0  1  1  1  0  1  X  1  0  1  1  1  X  X  1  1  X  0 X^2 X^2  1  0  1  0  X  X  1
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X  0  X  X  0 X^2 X^2 X^2+X  X  0  0  X X^2 X^2 X^2  0 X^2  X X^2 X^2+X  X X^2 X^2+X X^2+X  0  0 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2  X  X  X  X  X  0  0 X^2 X^2+X X^2
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  0 X^2+X X^2 X^2+X  X  X X^2  0 X^2  0 X^2+X X^2 X^2  X  X  X X^2  X X^2  0 X^2+X X^2 X^2+X  X  0 X^2+X X^2+X X^2 X^2 X^2 X^2+X  X  0 X^2+X X^2+X  X X^2+X  X  X  X X^2  X
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  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+138x^46+4x^47+297x^48+60x^49+409x^50+164x^51+454x^52+284x^53+524x^54+300x^55+507x^56+148x^57+334x^58+44x^59+213x^60+20x^61+110x^62+50x^64+17x^66+12x^68+4x^70+1x^72+1x^76

The gray image is a linear code over GF(2) with n=216, k=12 and d=92.
This code was found by Heurico 1.16 in 4.19 seconds.