The generator matrix

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

generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+350x^59+337x^60+344x^61+172x^62+280x^63+189x^64+244x^65+42x^66+38x^67+25x^68+20x^69+4x^75+2x^82

The gray image is a linear code over GF(2) with n=496, k=11 and d=236.
This code was found by Heurico 1.16 in 1.28 seconds.