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

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+48x^54+48x^55+108x^56+160x^57+42x^58+48x^59+36x^60+4x^62+13x^64+2x^66+2x^72

The gray image is a linear code over GF(2) with n=456, k=9 and d=216.
This code was found by Heurico 1.16 in 0.14 seconds.