The generator matrix

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

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+243x^56+128x^57+320x^58+128x^59+172x^60+16x^62+15x^64+1x^104

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 0.485 seconds.