The generator matrix

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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+360x^56+256x^57+512x^58+48x^59+304x^60+176x^61+256x^62+16x^63+97x^64+16x^65+4x^72+2x^80

The gray image is a linear code over GF(2) with n=472, k=11 and d=224.
This code was found by Heurico 1.16 in 44.5 seconds.