The generator matrix

 1  0  0  1  1  1  0 X^3  1  1 X^2 X^3+X^2  1  1 X^3+X^2+X  1  1 X^2+X  1 X^2+X  1 X^3+X^2+X  1  1 X^2+X  1 X^3+X^2+X  1  1  1 X^2  0  1 X^3+X^2  0 X^3  1 X^3+X  1 X^3+X^2+X  1 X^3+X^2+X  1  1  1 X^3+X^2+X  1  0 X^3+X  1  1  1 X^3+X^2+X  1
 0  1  0  0 X^2+1 X^2+1  1 X^3+X^2+X X^3 X^3+X^2+1  1  1 X^3+X^2 X^3+1 X^3+X X^2+X X+1  1  X  1 X^2+X+1  1 X^3+X^2+X X^3+X+1 X^2 X^2+X+1  1  X X^3+X^2+X+1  0 X^2  1  1  1 X^2+X X^3+X^2  1  X X^3+X^2+X X^3 X^3+X  1 X^3+X^2+1  X X^3 X^2+X X^2+X+1  1  1  1 X^3+X^2+X  X  1 X^3
 0  0  1 X+1 X^3+X+1 X^3 X^3+X^2+X+1  1 X^3+X^2+X X^2+1 X^3+X X^2+1 X^3+X^2+1  X  1 X^3+X+1 X^3+X^2  1 X^3+X X^3+X^2+X X^3+1 X^3+X^2+X+1 X^3 X^3+X  1 X+1 X^3 X^3+1 X^2 X^3+X^2+1  1 X^2+1 X^2+X+1 X^2+X+1  1  1 X^3+X^2  1  1  1  0 X^3+X^2+X+1 X^3+X^2+X+1 X^3+X+1 X^3+X+1  1 X^3+X X^3+X^2+X X^2+X X^3+X X^2+1 X^3+X^2+X+1 X^3+X+1  0
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  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+475x^50+888x^51+1212x^52+1200x^53+1299x^54+968x^55+782x^56+560x^57+401x^58+184x^59+138x^60+32x^61+33x^62+8x^63+9x^64+2x^68

The gray image is a linear code over GF(2) with n=432, k=13 and d=200.
This code was found by Heurico 1.16 in 8.08 seconds.