The generator matrix

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

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+396x^53+1072x^54+1584x^55+2014x^56+2226x^57+2440x^58+1998x^59+1834x^60+1318x^61+627x^62+436x^63+261x^64+70x^65+42x^66+30x^67+26x^68+6x^69+3x^70

The gray image is a linear code over GF(2) with n=464, k=14 and d=212.
This code was found by Heurico 1.16 in 7 seconds.