The generator matrix

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

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+160x^47+277x^48+522x^49+506x^50+804x^51+643x^52+852x^53+787x^54+916x^55+633x^56+710x^57+466x^58+418x^59+184x^60+148x^61+55x^62+42x^63+19x^64+20x^65+10x^66+10x^67+3x^68+4x^69+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 4.18 seconds.