The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  X  1  1  1  X  1 X^2+X  1  1  1  1 X^2 X^2  1  1  1  0 X^2  1  1  1  1  1  X  1  1  1  X  1  1  X  1  1  1 X^2+X  1  1  1  1  X  X  0  1  1 X^2
 0  1  1  0 X^2+X+1  1  X X+1  1  1 X^2+X X^2+1 X+1  1 X^2+X  1 X^2 X^2+1  X X+1  1  1  0  X X^2+1  1  1  1 X^2+X+1  X X^2+1  0  1 X^2+1 X^2 X^2+X+1  1 X^2+1 X^2+1  X X+1 X^2+X+1 X^2  1 X^2+X+1 X^2  1 X^2 X^2+X  X X^2 X^2 X+1  1
 0  0  X  0 X^2+X  0  0  0 X^2 X^2  0 X^2  X X^2+X  X X^2+X  X X^2+X  X X^2 X^2+X  X X^2+X  X  0 X^2  X  0 X^2+X  0  0 X^2  0 X^2+X X^2+X X^2+X  X X^2  0  0  X X^2  X  0 X^2 X^2+X X^2+X  X  X  X X^2  X  0  X
 0  0  0  X  0  0  X X^2 X^2+X  X  0  0  X  0 X^2+X X^2+X X^2  X  0 X^2+X X^2 X^2+X  X  0 X^2+X  X X^2 X^2+X X^2 X^2+X X^2 X^2  X  X X^2 X^2+X X^2 X^2 X^2+X X^2+X X^2  0 X^2+X X^2+X  X X^2+X X^2+X  X  X  X  X X^2+X X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0  0  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  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 46.

Homogenous weight enumerator: w(x)=1x^0+107x^46+92x^47+439x^48+276x^49+665x^50+480x^51+939x^52+676x^53+1018x^54+696x^55+811x^56+508x^57+612x^58+256x^59+290x^60+76x^61+117x^62+12x^63+76x^64+35x^66+3x^68+6x^70+1x^72

The gray image is a linear code over GF(2) with n=216, k=13 and d=92.
This code was found by Heurico 1.16 in 3.28 seconds.