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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+148x^57+68x^58+124x^59+40x^60+76x^61+12x^62+36x^63+5x^64+2x^72

The gray image is a linear code over GF(2) with n=472, k=9 and d=228.
This code was found by Heurico 1.16 in 0.422 seconds.