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

generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+20x^55+130x^56+96x^57+512x^58+136x^59+120x^60+4x^63+4x^64+1x^112

The gray image is a linear code over GF(2) with n=464, k=10 and d=220.
This code was found by Heurico 1.16 in 0.25 seconds.