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

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+52x^61+123x^62+124x^63+106x^64+188x^65+214x^66+178x^67+193x^68+186x^69+202x^70+150x^71+64x^72+64x^73+68x^74+34x^75+11x^76+16x^77+27x^78+22x^79+5x^80+4x^81+6x^82+4x^83+3x^84+2x^85+1x^108

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 48.2 seconds.