The generator matrix

 1  0  0  1  1  1 X^3  1  1  1  1  X X^3+X X^3+X^2 X^3+X  1  1  1  0  1 X^3+X^2+X  1 X^2+X X^3+X  1  1  1 X^2  0  1  X X^3  1  X  1 X^3+X^2+X X^3+X  1 X^2 X^3+X^2+X X^3  1  1 X^3+X  1  1  1  1 X^3+X^2  1  1  1  1  1 X^2+X X^3  1 X^3+X^2  1  1  1  1
 0  1  0 X^3 X^2+1 X^3+X^2+1  1  X X^3+X X^3+X^2+X+1 X^2+X+1  1 X^2  1  1 X^2+X X^3+X^2+1 X^3+1 X^3+X^2+X  0  1 X+1  1  1 X^2+X+1 X^3+X^2+X  X  1  1 X^2  0  1 X^3+X^2 X^3+X^2+X X+1  1  1  1  1  1  X X^3+X X+1  X X^3+X+1 X^3+X^2  1 X^2  1  X X^3 X^3+X^2+X X^2+1 X^3+X+1  1  1  0  1 X^3+1 X^3+X^2+1 X^2+X  0
 0  0  1 X^3+X+1 X+1 X^3 X^3+X+1 X^3+X X^3+1  1  X  X  1 X^3+1 X^2 X^3+X+1 X^3+X^2+X X^3+X^2+1  1 X^3+X X^3+1 X^3 X^3+X^2+X X+1 X+1 X^2+1  0 X^3+X^2+X X^2+X+1 X^3+1  1 X^2  X  1 X^3+X^2+X X^3+X^2 X^2+X+1 X^2+X X^3+X X^3+X^2+1  1 X+1 X^3+X^2+1  1 X^2 X^3+X^2+X+1 X^3+X+1 X+1  0 X^3+X^2 X^3+X^2+1 X^3+1 X^3+X^2 X^3+X+1 X^3+X+1 X^2+1 X^2 X+1 X^2+X+1 X^2+1 X^3+X^2+X  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+118x^58+572x^59+698x^60+712x^61+502x^62+416x^63+338x^64+296x^65+204x^66+80x^67+27x^68+88x^69+24x^70+12x^71+7x^72+1x^76

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 0.922 seconds.