The generator matrix

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

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+20x^55+4x^56+4x^57+2x^58+1x^60

The gray image is a linear code over GF(2) with n=432, k=5 and d=220.
This code was found by Heurico 1.16 in 0.063 seconds.