The generator matrix

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

generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+527x^58+980x^59+1318x^60+1124x^61+1079x^62+956x^63+817x^64+440x^65+349x^66+300x^67+181x^68+36x^69+61x^70+4x^71+17x^72+1x^76+1x^80

The gray image is a linear code over GF(2) with n=496, k=13 and d=232.
This code was found by Heurico 1.16 in 2.97 seconds.