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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+155x^68+444x^70+32x^71+681x^72+92x^73+1006x^74+320x^75+1388x^76+688x^77+1598x^78+936x^79+1789x^80+912x^81+1757x^82+656x^83+1313x^84+320x^85+895x^86+104x^87+600x^88+36x^89+351x^90+169x^92+83x^94+45x^96+10x^98+2x^100+1x^116

The gray image is a linear code over GF(2) with n=320, k=14 and d=136.
This code was found by Heurico 1.16 in 27.3 seconds.