The generator matrix

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

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+176x^53+233x^54+274x^55+613x^56+650x^57+623x^58+344x^59+460x^60+300x^61+141x^62+82x^63+72x^64+74x^65+26x^66+20x^67+6x^68+1x^90

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 0.406 seconds.