The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^2+X  1  1 X^3+X^2 X^2+X  1  1  1  0 X^3+X^2  1 X^2  X  1  1 X^3+X^2  1 X^2 X^3+X^2+X  1 X^3  1 X^3+X  1  1 X^3+X  1  1  1 X^3+X^2+X X^3+X X^3  1 X^3 X^3+X^2  1  1  0  1 X^3+X^2  X  X X^2  1
 0  1  0  0  0 X^3+1 X^3+1  1 X^3+X^2+X X^3+X X^3+X^2+X X+1 X^3+X^2+X+1  1  1 X^2+1  0 X^3  X X^2+X X^3+X^2+1  1  1 X^2+X+1 X^3+X^2  1 X^2+X+1 X^3+X^2  1 X+1  1  X  1 X^3 X^3+X^2+X+1  1 X^3+X+1  1 X^3  1  1  1 X+1 X^2+X  1 X^3+X^2+X  X  1 X^3+X^2+X+1 X^3  1  X  1 X^3+X^2
 0  0  1  0  1  1 X^2 X^2+1  0 X^3+1  1 X^2+1 X^2+X X^3+X^2+X+1 X^3 X^2  1  X  1  1  1  X X^2+1 X^3+X^2+X X^2+X X+1  1  X X^3+X^2 X^3+X^2+1 X^2+X X^3+X^2+X+1 X^2+X+1 X+1 X^3 X^2+X+1  0 X^2+X+1 X^2+X+1 X^2+X X^2+X X^2+X+1 X^2  1  0 X^3+X^2+X+1 X^3 X^3+X^2 X+1  1 X^3+X^2  0 X^3+X^2+X+1  0
 0  0  0  1  1 X^2 X^2+1  1 X^2+X+1 X^3+X X^2+1 X^2+1 X^2+X X^3+X^2+X X^2+1 X^2+X+1 X^3+X^2+X+1 X^3+1 X^3+X^2+X+1  0 X^3+1 X+1 X^2+X  0 X^3+X^2 X^3+X^2+X+1 X^3+X  1 X^3+X^2+X+1 X^3 X^2 X^3 X^3+X^2+X X^3+X+1 X^3+X X^3+1 X^2  0  X X^3+X^2+X+1 X+1 X^2 X^3+X^2+X+1 X^3+X^2+1 X^2  1  X X^3+X^2+X X^2+X+1 X^3 X^3  1 X^3 X^2
 0  0  0  0 X^3+X^2  0 X^3+X^2  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^2 X^2 X^3+X^2 X^2 X^2 X^2 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2  0 X^3 X^2  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2  0 X^3 X^2 X^3 X^3+X^2 X^3  0  0 X^3+X^2

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+203x^46+1138x^47+3279x^48+6454x^49+11998x^50+20426x^51+29797x^52+36998x^53+40821x^54+37410x^55+31123x^56+20118x^57+11813x^58+6106x^59+2617x^60+1210x^61+368x^62+164x^63+61x^64+20x^65+13x^66+4x^67+2x^68

The gray image is a linear code over GF(2) with n=432, k=18 and d=184.
This code was found by Heurico 1.16 in 424 seconds.