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  0  X  X  1 X^2  0  1  1  0  X  1  1  1  0  1  1  X X^2  1  1  X  0  1 X^2 X^2  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X  0 X^2+X X^2+X  0 X^2+X X^2  0 X^2+X X^2+X X^2+X  0  X X^2+X X^2 X^2  X  0  X X^2+X  X  X  X  X  X  X X^2  0  X  X  0 X^2  0 X^2  X X^2  X X^2
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X  0 X^2  0  0 X^2  X  X X^2+X  X X^2+X X^2  0  X  X  X X^2+X X^2  0 X^2  X X^2+X X^2 X^2+X  X  0  0  X X^2+X  X X^2+X X^2 X^2+X X^2 X^2  X X^2  0
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2 X^2+X  0 X^2+X X^2+X  X  X  X X^2+X X^2  0  0  X X^2 X^2 X^2  X  0 X^2 X^2+X X^2  0  0  0  0 X^2+X  0  X X^2+X  0 X^2 X^2  X  0 X^2+X  0  X
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 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  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 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+119x^46+303x^48+68x^49+365x^50+176x^51+509x^52+260x^53+600x^54+288x^55+460x^56+172x^57+302x^58+48x^59+198x^60+12x^61+135x^62+51x^64+13x^66+13x^68+2x^70+1x^80

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 1.08 seconds.