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

generates a code of length 68 over Z2[X]/(X^3) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+70x^61+99x^62+128x^63+143x^64+138x^65+180x^66+194x^67+219x^68+202x^69+183x^70+136x^71+93x^72+72x^73+59x^74+34x^75+21x^76+20x^77+14x^78+20x^79+2x^80+10x^81+9x^82+1x^112

The gray image is a linear code over GF(2) with n=272, k=11 and d=122.
This code was found by Heurico 1.16 in 29.7 seconds.