The generator matrix

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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+111x^48+248x^49+390x^50+346x^51+508x^52+394x^53+438x^54+296x^55+385x^56+260x^57+256x^58+132x^59+134x^60+66x^61+67x^62+40x^63+9x^64+8x^65+2x^67+4x^68+1x^70

The gray image is a linear code over GF(2) with n=216, k=12 and d=96.
This code was found by Heurico 1.16 in 0.622 seconds.