The generator matrix

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

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+335x^70+352x^71+715x^72+488x^73+875x^74+544x^75+786x^76+528x^77+773x^78+416x^79+617x^80+348x^81+513x^82+208x^83+281x^84+120x^85+136x^86+48x^87+62x^88+20x^89+24x^90+1x^92+1x^96

The gray image is a linear code over GF(2) with n=308, k=13 and d=140.
This code was found by Heurico 1.16 in 4.62 seconds.