The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+43x^70+78x^71+189x^72+188x^73+436x^74+378x^75+709x^76+442x^77+813x^78+480x^79+768x^80+488x^81+883x^82+422x^83+695x^84+326x^85+325x^86+144x^87+148x^88+78x^89+40x^90+24x^91+30x^92+8x^93+17x^94+10x^95+13x^96+6x^97+1x^98+5x^100+2x^102+1x^104+1x^108

The gray image is a linear code over GF(2) with n=320, k=13 and d=140.
This code was found by Heurico 1.16 in 5.54 seconds.