The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  X  X X^2 X^2+X  1 X^2  X  1  1 X^2  1  1  1  X  0  1  0 X^2  1  1 X^2+X  1  1  1 X^2  X  1 X^2+X  1  X  X  1  1  1  1  1 X^2+X  1  1  1  0  1  0  1 X^2  0  X  X X^2+X  X  1 X^2+X  1  0  0  1  1  1  1  1 X^2+X  1  1 X^2 X^2 X^2  1  0  1
 0  1  0  0  X  1 X^2+X+1 X^2 X^2+X X+1 X^2+1  1  1  1 X^2+X X^2  1  1 X^2  X  1 X^2+1 X^2+X X+1 X^2+X  1 X^2+1 X^2+X  0 X+1 X^2+X  1 X^2+X X+1 X^2+X+1  1  X X^2+X  1 X^2+X+1 X^2  1 X^2 X^2+1  1 X^2+1 X^2  1 X^2+X  X X^2 X^2  0 X^2 X+1 X^2+X  1  1  0 X^2+X  0 X^2+1 X^2 X^2  1  1  1 X^2+X  1  1  1 X^2 X^2+X+1 X^2+X+1  1  1  1  X  1  0
 0  0  1  0  0  0  0  1 X^2+1  1  1 X+1  1  X  1 X^2  X X+1  X X^2+X+1 X^2  1 X+1 X^2+X X^2+X X^2+1 X+1  1  1 X^2+X  0  0  1 X^2 X^2  X  1 X^2 X^2+X+1  1  0 X^2+1  1 X+1  0  0 X^2+X+1  0  X X^2+1 X^2+X  X  X  1 X^2+1  1  X  0  1  1  1 X^2  1  X  X X^2+1 X^2 X^2 X^2+1  X X^2+X X^2+X X+1 X^2+1  X X^2+X+1  0 X^2+X+1  1  X
 0  0  0  1  1 X^2+X+1 X^2+X X+1  0  1 X^2+X  1 X^2 X+1 X^2+1 X^2+1  X X^2+X+1  X X^2+X+1 X^2+X+1 X^2+X+1  0  X  1 X^2  X  0 X^2+1 X^2+1 X+1  X  X X^2  1  1 X+1 X^2+X X+1 X^2+X  1 X^2+X X^2+X  0 X^2+1  X X^2  1 X^2  1  X  1  1 X^2+X X^2 X+1  0  1 X^2+1  0 X+1  0 X+1 X^2 X+1 X^2+X+1 X+1 X+1  0 X^2+X X^2+X+1  1 X^2+1 X^2+X+1 X^2 X^2+X X+1 X^2 X^2  1
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0 X^2  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  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  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+178x^70+356x^71+921x^72+928x^73+1621x^74+1528x^75+2306x^76+2068x^77+2574x^78+2298x^79+3186x^80+2422x^81+2677x^82+2068x^83+2520x^84+1400x^85+1404x^86+806x^87+698x^88+320x^89+212x^90+98x^91+87x^92+28x^93+31x^94+12x^95+6x^96+2x^97+6x^98+2x^99+3x^100+1x^102

The gray image is a linear code over GF(2) with n=320, k=15 and d=140.
This code was found by Heurico 1.16 in 54.2 seconds.