The generator matrix

 1  0  0  1  1  1  X  1  1 X^2  1  X  1 X^2+X  1  1  1 X^2  1 X^2 X^2 X^2+X X^2+X  1  1  1  1 X^2+X X^2+X  1  0  1  1  1  1  1  X  0  1  1  0  0  1  0  1 X^2  1  X X^2  1  1  1 X^2+X  0  1  1  1  1  1  X X^2+X  1  1  0  1  X  1  0  1  1  1  1  1  0  1 X^2+X  1 X^2+X  1  1
 0  1  0  0  1 X^2+X+1  1  X X^2+X+1  1 X+1 X^2+X X^2+X  1  1 X^2+1 X^2+X  1 X^2+X  1 X^2+X  0  1  0 X^2+1 X^2 X^2+X X^2  1 X+1  1 X+1  X X^2+1 X^2+1 X^2  1  0 X^2  X  1  1  1  X X+1 X^2  X  1  1 X^2+1 X^2+X+1 X^2+X+1  1  X X^2+X+1 X^2 X^2  X  X X^2  X  0  1  1  0 X^2 X^2  1 X^2+X X^2+X+1  X X^2 X^2+X  0  0 X^2+X X^2+1  1 X^2+X  0
 0  0  1 X+1 X^2+X+1 X^2+X  1  X X^2+1 X^2+1 X^2  1 X+1 X^2+X  1  0  0 X^2+X X^2+1 X+1  1  1 X^2+X+1 X+1 X^2 X^2+X X+1  1  0 X+1 X^2+X X+1 X^2+X X^2+X X^2+X+1 X^2+1 X+1  1 X^2 X^2  X X^2+1 X^2+X+1  1  1  1 X^2+1  0 X^2+X X^2+X X^2 X^2 X^2  1 X^2+X+1  0 X^2+X+1  0  0  1  1 X^2+X+1 X^2+X+1 X+1  0  1 X^2+X+1 X+1 X^2+1 X^2+1 X+1 X^2+X X+1  1 X^2+X  1 X^2+X+1 X^2  X X+1
 0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 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 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  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 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 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+177x^72+108x^73+622x^74+272x^75+921x^76+324x^77+1046x^78+344x^79+1011x^80+396x^81+861x^82+248x^83+648x^84+172x^85+417x^86+136x^87+254x^88+24x^89+105x^90+24x^91+40x^92+21x^94+17x^96+3x^100

The gray image is a linear code over GF(2) with n=320, k=13 and d=144.
This code was found by Heurico 1.16 in 4.97 seconds.