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  1  1  1  1  1  1  1  1  X  1  1  1  1 X^2  1  1  1  1  X  1  1  1  X  1
 0  X  0  0  0  X X^2+X  X  0 X^2  X X^2+X  0 X^2  X  X  0 X^2  X  X X^2+X X^2 X^2+X  0 X^2+X  X X^2  0 X^2 X^2+X  X  0 X^2 X^2 X^2 X^2 X^2+X  X  X X^2+X X^2 X^2  X X^2 X^2+X X^2  X  X X^2+X X^2+X X^2+X  X  X X^2+X  X X^2+X  X  0  X X^2+X  0 X^2
 0  0  X  0  X  X  X X^2  0 X^2 X^2+X X^2+X  X  X X^2 X^2  0 X^2+X  0  X  X  X  0  0 X^2+X X^2+X X^2+X X^2  0 X^2  0  X  X X^2+X X^2 X^2 X^2 X^2  0  0 X^2+X  0  X  0 X^2+X  X X^2+X X^2+X  0 X^2+X  X  X X^2  X X^2  0 X^2+X X^2+X  X X^2+X X^2  X
 0  0  0  X  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2+X  X  0  X  0 X^2 X^2+X X^2+X  0 X^2+X X^2  0 X^2+X  0  X  X X^2 X^2+X X^2+X  0 X^2  0 X^2  0 X^2 X^2  0 X^2+X X^2+X  X  X  X  X  X  X X^2  0  X X^2 X^2  0 X^2+X  0  X X^2+X X^2  0 X^2+X X^2  X  0
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  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+32x^56+68x^57+45x^58+56x^59+110x^60+136x^61+168x^62+120x^63+95x^64+76x^65+20x^66+48x^67+11x^68+8x^69+20x^70+4x^72+3x^74+2x^76+1x^116

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 0.199 seconds.