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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+16x^50+24x^51+35x^52+104x^53+148x^54+104x^55+43x^56+24x^57+11x^58+1x^60+1x^106

The gray image is a linear code over GF(2) with n=216, k=9 and d=100.
This code was found by Heurico 1.16 in 0.072 seconds.