The generator matrix

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

generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+14x^56+104x^57+314x^58+392x^59+334x^60+592x^61+594x^62+608x^63+379x^64+376x^65+232x^66+88x^67+38x^68+16x^69+10x^70+2x^74+2x^88

The gray image is a linear code over GF(2) with n=496, k=12 and d=224.
This code was found by Heurico 1.16 in 0.328 seconds.