The generator matrix

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

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+626x^55+745x^56+762x^57+454x^58+482x^59+345x^60+258x^61+135x^62+152x^63+44x^64+84x^65+1x^66+4x^67+1x^70+1x^74+1x^76

The gray image is a linear code over GF(2) with n=464, k=12 and d=220.
This code was found by Heurico 1.16 in 84.2 seconds.