The generator matrix

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

generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+80x^61+167x^62+180x^63+191x^64+192x^65+178x^66+152x^67+175x^68+182x^69+155x^70+164x^71+100x^72+52x^73+35x^74+14x^75+12x^76+2x^77+1x^78+2x^81+6x^82+1x^84+1x^86+2x^89+1x^90+2x^91

The gray image is a linear code over GF(2) with n=268, k=11 and d=122.
This code was found by Heurico 1.16 in 7.1 seconds.