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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+45x^72+70x^73+116x^74+66x^75+181x^76+82x^77+275x^78+56x^79+342x^80+76x^81+293x^82+32x^83+137x^84+48x^85+52x^86+32x^87+51x^88+38x^89+20x^90+6x^91+9x^92+6x^93+9x^94+1x^96+2x^98+1x^100+1x^130

The gray image is a linear code over GF(2) with n=320, k=11 and d=144.
This code was found by Heurico 1.16 in 0.74 seconds.