The generator matrix

 1  0  0  0  1  1  1  0  0 X^2  1  1  1  1 X^2+X X^2  1 X^2+X  1 X^2+X X^2  1  1  X  1  X  1  0  1  1  1  1 X^2  0  1  1  X X^2+X  1  1 X^2  X  1 X^2  1 X^2+X  1  X  1  1  1  X  1  0  X  1  1  1  X  1  1  1
 0  1  0  0  0 X^2 X^2 X^2  1  1 X+1  1  1 X^2+1  1  1  X X^2+X  1  0  1 X+1 X^2+X  1 X^2+X  1 X+1  X X^2+X X+1 X^2  1  1  1 X^2 X^2+X X^2+X  1 X^2+X X+1  X  0 X+1  0 X^2+1  1  0  1  1 X+1 X^2+X+1  1  0  X  1 X^2+X+1 X^2+1  1  0  1 X+1 X^2
 0  0  1  0 X^2  1 X^2+1  1 X+1  0  1 X^2+X X^2 X+1 X+1  X  0  1 X+1  1 X^2+1 X^2+X X^2+1 X^2 X^2+X+1  1 X^2+1 X^2  X  X X^2+X  1 X^2+X X^2+1  0  X X^2 X^2+X X+1 X+1  1  1 X^2  1  1 X^2 X^2+X  X  X  0 X^2 X^2+X+1  0  1 X+1 X^2+1 X+1 X^2+1  1 X^2+X+1 X+1  X
 0  0  0  1 X^2+X+1 X^2+X+1  0 X+1 X^2  1  1  1 X^2  0 X^2+X+1 X^2 X^2  1 X^2+1 X^2 X^2+X+1 X^2+X+1  1 X^2+X+1 X^2+X  X  X  1 X+1 X^2+X X^2+1 X^2+X X^2+1  X  X X^2+1  1 X^2 X^2 X^2+1 X^2+X X^2+X+1  1  1 X^2+X+1 X^2 X+1  1 X^2+X+1 X^2+X+1  1 X+1  X  0 X^2+X X+1 X+1  0  0 X^2+X X^2+X  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+122x^56+316x^57+390x^58+418x^59+404x^60+406x^61+392x^62+310x^63+280x^64+256x^65+214x^66+194x^67+158x^68+102x^69+57x^70+18x^71+11x^72+24x^73+18x^74+4x^75+1x^78

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 0.631 seconds.