The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X^3+X  1  1  1  1 X^2 X^3+X^2+X  1  1  X  1  1  X  1  1 X^2 X^3  X  1  1  1  1  1  1  1  1  0 X^3+X^2+X X^3  1  1  1 X^2  1  X  1  1  1 X^2+X X^3+X  1  1  1  0  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2 X^3+1  1 X+1 X^3+X^2+X  1  1  0 X^3+X^2+1 X^3 X^3+1  1  1 X^3+X^2+1 X^2+X+1  1 X^3+X^2  X  1  X X+1  1  1  1 X^3+X^2+X+1 X^2+1  0 X^3+X^2 X^3+X+1 X^3+X^2 X^3+X X^3+X^2+X  1  1  1 X^2+X+1 X^2+X X^3+1  1  0  1 X^2+X+1  1 X^3+X^2+X+1  1  1 X^2 X^3+X^2+1 X^3+X+1  X  0 X^2+X
 0  0  X  0 X^3+X  X X^3+X X^3  0 X^3 X^3+X X^3+X^2+X X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2+X X^3+X^2  X X^3+X^2  X  0 X^3+X^2+X  0 X^3+X^2 X^3+X^2+X  X X^3+X^2 X^3+X^2+X X^3  0 X^3+X X^2+X X^2+X X^2 X^3+X^2+X X^3+X^2 X^3+X^2+X  X X^3 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2+X  X X^3+X X^3+X^2+X X^3+X^2+X X^2+X  0  0 X^2+X X^3 X^3+X  0 X^3+X^2+X
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 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+251x^54+508x^55+559x^56+544x^57+519x^58+552x^59+467x^60+368x^61+193x^62+60x^63+26x^64+16x^65+17x^66+8x^68+4x^70+3x^76

The gray image is a linear code over GF(2) with n=464, k=12 and d=216.
This code was found by Heurico 1.16 in 0.328 seconds.