The generator matrix

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

generates a code of length 58 over Z2[X]/(X^4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+54x^53+245x^54+462x^55+525x^56+544x^57+544x^58+496x^59+528x^60+396x^61+132x^62+82x^63+62x^64+12x^65+5x^66+2x^68+2x^69+2x^72+1x^78+1x^82

The gray image is a linear code over GF(2) with n=464, k=12 and d=212.
This code was found by Heurico 1.16 in 0.297 seconds.