The generator matrix

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

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+50x^56+288x^57+76x^58+192x^59+76x^60+288x^61+50x^62+1x^64+2x^86

The gray image is a linear code over GF(2) with n=472, k=10 and d=224.
This code was found by Heurico 1.16 in 0.125 seconds.