The generator matrix

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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+152x^47+245x^48+580x^49+485x^50+886x^51+551x^52+1032x^53+562x^54+936x^55+577x^56+812x^57+371x^58+502x^59+201x^60+128x^61+49x^62+78x^63+21x^64+8x^65+4x^66+4x^67+4x^68+1x^70+2x^71

The gray image is a linear code over GF(2) with n=216, k=13 and d=94.
This code was found by Heurico 1.16 in 2.74 seconds.