The generator matrix

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

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+344x^51+226x^52+472x^53+64x^54+428x^55+212x^56+224x^57+52x^59+6x^60+8x^61+4x^63+1x^64+4x^67+2x^72

The gray image is a linear code over GF(2) with n=432, k=11 and d=204.
This code was found by Heurico 1.16 in 131 seconds.