The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  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  1  1  1  X  1  1  1  1  1  1  X  1  1  1  1  1  X  1  X  1
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X  0 X^2  X  X X^2+X X^2  0 X^2+X X^2+X  0  0 X^2+X  0 X^2  X  X X^2  0  X  X  0 X^2  X  0 X^2  X  X  X X^2+X  X X^2+X X^2+X X^2+X  X  X X^2  0  0 X^2+X X^2 X^2+X X^2+X X^2  0  X X^2 X^2+X X^2+X  0  X
 0  0  X  X  0 X^2+X  X X^2  0  X  X  0 X^2  X X^2+X  0 X^2 X^2+X  0 X^2+X X^2  X  0  X  0  X X^2+X X^2 X^2  X X^2+X  0  0  X  X X^2+X  0 X^2 X^2+X  X  0  0 X^2 X^2+X X^2+X X^2+X  0 X^2 X^2 X^2+X  0  X  X X^2  X X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2+X
 0  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0  0  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+21x^56+48x^57+81x^58+64x^59+126x^60+24x^61+333x^62+28x^63+138x^64+44x^65+20x^66+32x^67+29x^68+8x^69+7x^70+4x^71+4x^72+4x^73+6x^74+1x^76+1x^114

The gray image is a linear code over GF(2) with n=248, k=10 and d=112.
This code was found by Heurico 1.16 in 0.202 seconds.