The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^54+9x^56+6x^60

The gray image is a linear code over GF(2) with n=432, k=6 and d=216.
This code was found by Heurico 1.16 in 0.078 seconds.