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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+98x^55+107x^56+60x^57+164x^58+182x^59+132x^60+182x^61+208x^62+236x^63+212x^64+108x^65+101x^66+76x^67+52x^68+24x^69+24x^70+34x^71+7x^72+8x^73+14x^74+14x^75+2x^77+1x^82+1x^96

The gray image is a linear code over GF(2) with n=248, k=11 and d=110.
This code was found by Heurico 1.16 in 60.6 seconds.