The generator matrix

 1  0  1  1  1  0  1 X^2+X  1  1 X^2+X  1  1 X^2  1  1  1 X^2  X  1  X  1  1  X  1  1  X  1  1  0  1  X  1  1  0  1  1  1 X^2 X^2  0 X^2  1  1  1  1  1  1  1  1  1  1  0  1
 0  1  1  0 X^2+X+1  1  X  1 X^2+X+1  X  1  1 X^2  1 X+1  0 X^2+X+1  1  1 X^2+X  1 X^2+1  X  1 X^2+X+1  1  1  1 X^2+X+1  1 X^2+X+1  1 X^2  X  1 X+1  0  1  1  1  1  1  X X^2+X+1 X^2+1  1 X^2  0 X^2+X X^2 X^2  0  1  X
 0  0  X  0 X^2+X  X  0  X  0  X X^2  0  X  0 X^2 X^2+X  X  X X^2+X X^2  0 X^2+X  X  0 X^2 X^2 X^2+X  X X^2 X^2  0  X X^2 X^2+X X^2 X^2+X X^2  X  0  X X^2 X^2 X^2  X X^2+X  0  X X^2+X  X X^2 X^2 X^2  X X^2+X
 0  0  0  X  0  X  X  X X^2+X  0 X^2 X^2+X X^2  X X^2  X X^2+X X^2 X^2  0 X^2+X X^2+X X^2+X X^2 X^2+X X^2  0  X X^2+X X^2+X  0 X^2  X X^2  0  X X^2 X^2  X  X X^2  0  X  0 X^2  0 X^2+X  X  0  X  0  0  X  X
 0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  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+38x^48+156x^49+141x^50+272x^51+140x^52+236x^53+168x^54+228x^55+121x^56+232x^57+106x^58+124x^59+26x^60+12x^61+11x^62+12x^63+3x^64+4x^65+4x^66+4x^67+6x^68+1x^70+1x^72+1x^74

The gray image is a linear code over GF(2) with n=216, k=11 and d=96.
This code was found by Heurico 1.16 in 0.239 seconds.