The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+43x^70+90x^71+158x^72+166x^73+204x^74+182x^75+124x^76+170x^77+120x^78+174x^79+187x^80+154x^81+129x^82+58x^83+33x^84+22x^85+10x^86+8x^87+4x^88+2x^90+2x^92+1x^94+2x^96+1x^98+1x^100+1x^102+1x^110

The gray image is a linear code over GF(2) with n=308, k=11 and d=140.
This code was found by Heurico 1.16 in 0.493 seconds.