The generator matrix

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

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+85x^56+126x^57+183x^58+222x^59+169x^60+206x^61+172x^62+164x^63+175x^64+152x^65+140x^66+122x^67+75x^68+26x^69+11x^70+2x^71+6x^72+1x^74+2x^79+1x^80+2x^81+4x^82+1x^86

The gray image is a linear code over GF(2) with n=248, k=11 and d=112.
This code was found by Heurico 1.16 in 0.328 seconds.