The generator matrix

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

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+96x^56+112x^57+274x^58+336x^59+531x^60+424x^61+598x^62+512x^63+468x^64+288x^65+194x^66+112x^67+89x^68+8x^69+28x^70+7x^72+8x^74+7x^76+2x^78+1x^92

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 0.609 seconds.