The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+187x^56+184x^57+428x^58+412x^59+438x^60+360x^61+414x^62+380x^63+327x^64+212x^65+210x^66+140x^67+147x^68+72x^69+104x^70+28x^71+30x^72+4x^73+6x^74+3x^76+6x^78+3x^80

The gray image is a linear code over GF(2) with n=248, k=12 and d=112.
This code was found by Heurico 1.16 in 1.15 seconds.