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

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+87x^56+848x^58+87x^60+1x^116

The gray image is a linear code over GF(2) with n=464, k=10 and d=224.
This code was found by Heurico 1.16 in 0.219 seconds.