The generator matrix

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

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+151x^50+124x^51+331x^52+296x^53+393x^54+228x^55+234x^56+88x^57+105x^58+28x^59+57x^60+7x^62+4x^63+1x^88

The gray image is a linear code over GF(2) with n=432, k=11 and d=200.
This code was found by Heurico 1.16 in 0.171 seconds.