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

generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+156x^56+96x^57+104x^58+88x^60+32x^61+24x^62+7x^64+4x^72

The gray image is a linear code over GF(2) with n=464, k=9 and d=224.
This code was found by Heurico 1.16 in 0.172 seconds.