The generator matrix

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

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+137x^72+212x^73+582x^74+312x^75+751x^76+536x^77+914x^78+496x^79+731x^80+564x^81+682x^82+416x^83+565x^84+308x^85+372x^86+160x^87+240x^88+40x^89+76x^90+24x^91+28x^92+4x^93+22x^94+11x^96+8x^98

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 4.66 seconds.