The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  X  1  1  1 X^3  1  1  1 X^3+X^2  1  1  X  1  1  1  1  X  1  1 X^2 X^2  1 X^3  1 X^3+X^2 X^3  X  X  1
 0  X  0  X  0 X^3 X^3+X  X X^2 X^2+X X^2 X^2+X X^2 X^3+X^2+X X^3+X^2 X^2+X X^2 X^3+X^2+X X^3 X^2+X X^3+X  X X^2+X  0 X^3+X^2 X^2 X^3+X X^3+X X^2 X^3+X X^2 X^3 X^3+X X^2 X^3+X^2 X^2+X X^3+X^2  X X^2 X^3+X^2  X X^2 X^2+X  X  X X^3+X^2+X X^3  X  X  X X^3+X^2  X X^3  X  X  0 X^3+X X^3+X^2
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^2 X^2 X^3+X^2+X  X  0 X^3 X^3+X X^2+X X^3+X^2  X  0 X^2+X X^2 X^3+X X^3+X  X  0 X^3 X^3+X^2+X X^2+X X^3+X^2  X X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X  X  0 X^2 X^2+X X^3 X^2 X^2 X^2 X^2+X X^3+X  0 X^3 X^3 X^2+X X^3+X^2+X X^3+X X^3+X  X  X X^2+X  0  0 X^2+X X^3 X^2+X
 0  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0
 0  0  0  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  0  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 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+164x^53+212x^54+452x^55+363x^56+754x^57+463x^58+666x^59+288x^60+288x^61+135x^62+168x^63+51x^64+34x^65+21x^66+26x^67+8x^69+1x^70+1x^88

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 0.422 seconds.