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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+86x^70+130x^72+40x^74+88x^76+719x^78+685x^80+72x^82+40x^84+81x^86+65x^88+25x^94+14x^96+1x^102+1x^136

The gray image is a linear code over GF(2) with n=316, k=11 and d=140.
This code was found by Heurico 1.16 in 97.2 seconds.