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

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+47x^46+4x^47+131x^48+28x^49+223x^50+84x^51+251x^52+140x^53+266x^54+140x^55+250x^56+84x^57+192x^58+28x^59+110x^60+4x^61+29x^62+16x^64+9x^66+6x^68+2x^70+2x^72+1x^84

The gray image is a linear code over GF(2) with n=216, k=11 and d=92.
This code was found by Heurico 1.16 in 0.354 seconds.