The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+84x^71+165x^72+206x^73+466x^74+366x^75+701x^76+420x^77+856x^78+484x^79+906x^80+522x^81+815x^82+406x^83+589x^84+310x^85+351x^86+138x^87+166x^88+52x^89+49x^90+44x^91+17x^92+22x^93+19x^94+14x^95+14x^96+4x^97+2x^98+2x^102+1x^108

The gray image is a linear code over GF(2) with n=320, k=13 and d=142.
This code was found by Heurico 1.16 in 6.59 seconds.