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

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+136x^55+22x^56+206x^57+30x^58+96x^59+8x^60+8x^63+1x^64+2x^66+2x^73

The gray image is a linear code over GF(2) with n=456, k=9 and d=220.
This code was found by Heurico 1.16 in 0.797 seconds.