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

generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+116x^54+222x^55+153x^56+436x^57+232x^58+400x^59+155x^60+204x^61+98x^62+18x^63+10x^64+1x^70+1x^84+1x^86

The gray image is a linear code over GF(2) with n=464, k=11 and d=216.
This code was found by Heurico 1.16 in 0.141 seconds.