The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X^3+X  1  1  1  1 X^2 X^3+X^2+X  1  1  X  1  1  X  1  1 X^2 X^3  1  X  1  0  1 X^3+X^2+X  1  1  1 X^2+X  0  1  0  1  1  1  1 X^3+X^2+X  X  1  1 X^3+X^2  1  1  1  1  1  1 X^3+X^2+X X^2 X^3+X^2 X^3 X^3+X^2+X
 0  1  1 X^2+X  1 X^2+X+1 X^2 X^3+1  1 X+1 X^3+X^2+X  1  1  0 X^3+X^2+1 X^3 X^3+1  1  1 X^3+X^2+1 X^2+X+1  1 X^3+X^2  X  1  X X+1  1  1 X^2+X  1 X^3+X+1  1 X^2+X+1  1  X X^2+1 X^3+X^2+X+1  1  1 X^2+X  1  1 X^2 X^2+X+1 X^2  1  1 X^3+X^2+X X^3  1 X^3+X^2+1  1 X^2+X+1 X^3+X^2+1 X^3 X^2+1  1  1  1 X^2  1
 0  0  X  0 X^3+X  X X^3+X X^3  0 X^3 X^3+X X^3+X^2+X X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2+X X^3+X^2  X X^3+X^2  X  0 X^3+X^2+X  0 X^3+X^2 X^3+X^2+X  X X^3+X^2 X^3+X^2+X X^2+X X^3+X^2 X^3 X^3+X^2+X  X X^3  0 X^3 X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X^2 X^2 X^3+X  X X^2  X X^2 X^3+X X^2+X X^3  X X^3+X^2+X X^3+X X^2+X X^2  0 X^3+X^2+X X^3+X^2 X^3+X^2+X  X X^2+X
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0  0  0  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  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+310x^58+402x^59+730x^60+416x^61+566x^62+372x^63+644x^64+264x^65+250x^66+58x^67+36x^68+24x^69+4x^70+12x^72+5x^74+1x^82+1x^88

The gray image is a linear code over GF(2) with n=496, k=12 and d=232.
This code was found by Heurico 1.16 in 0.39 seconds.