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  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^2 X^3 X^2  0 X^3 X^3 X^3+X^2 X^2 X^2  0 X^3+X^2 X^3+X^2
 0  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  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  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3  0 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  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3
 0  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  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+37x^56+144x^58+640x^59+179x^60+16x^62+6x^64+1x^116

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 0.188 seconds.