The generator matrix

 1  0  0  0  1  1  1  1  1  1  1 X^2  X  0 X^2 X^2+X X^2 X^2+X  1  1  1  X  1  X  1  1 X^2+X  X  1 X^2  1  1 X^2  1  1 X^2+X  0  1  1  X  1  1  1  1  1  X X^2+X X^2+X  0  1  0  1  1 X^2 X^2+X  X  0  0  1 X^2 X^2+X  1  1 X^2+X X^2 X^2 X^2  1  1  1  X  0 X^2+X  1  1  X  1  1  1  1
 0  1  0  0  0  0  1 X^2+X+1  1  1 X^2+X  1  1 X^2+X  1  1  X  1 X+1 X^2+X X^2+X+1  0 X+1  1  1  0  1 X^2  0 X^2+X  X X^2  1 X^2 X^2+X+1 X^2  1 X+1 X^2+1  1 X^2+X+1 X^2 X+1 X+1 X+1  1  1  1  X  X  1 X^2+1 X^2 X^2 X^2+X  0  X  1 X^2+X  1  1 X^2 X^2+X  1  1  1  X X^2+1 X^2+1 X^2+1  1  1  0 X^2 X^2+X  1  X X^2 X^2+1  0
 0  0  1  0  0  1  0  1 X^2+1 X^2  1 X^2+X+1 X^2+1  1 X^2+X  1  1 X+1 X^2  X X+1 X^2+X X^2 X^2  1 X+1  0  1  X  1 X^2+X+1  X X^2+1  X X+1  1 X^2+X  0  0 X+1 X^2 X^2 X^2 X+1 X+1 X^2+X X^2 X^2+1  X X^2+X+1 X^2+X X+1 X^2+X+1  1  1  1 X^2 X^2 X^2+X X^2+X X+1 X^2  1  X X^2 X^2+X+1  1  1 X^2+X  X  0 X^2+X+1  1  X  0  0 X^2+X+1 X^2+1 X^2 X^2
 0  0  0  1  1 X+1 X^2+X+1 X^2+1 X^2  X X^2+X X^2+1 X^2+X X+1 X^2+X+1  1 X^2+1 X^2 X^2+X X^2+1  0  1 X^2+1  1 X^2+1  0 X^2  X X^2  X X+1 X+1 X^2+1 X^2+1 X^2+X X^2+X+1  0 X^2+1  X  0 X+1  0  0 X^2+X  1  1  X X^2  1 X+1 X^2+X+1 X+1 X+1 X^2+X+1 X^2+X X^2+1  1  1  0  0 X^2+1  X  X  0 X+1  1 X^2+X+1 X+1 X^2+1 X^2  1 X^2+X+1 X+1 X^2  0 X^2+1  0 X^2  X  0
 0  0  0  0  X  X  X  X  0  0  0 X^2+X  0 X^2+X X^2+X  X X^2+X  0 X^2 X^2+X X^2 X^2+X X^2+X  X  X X^2  0  0  0 X^2  X  X  X  X  X  0 X^2+X X^2 X^2+X  X  0 X^2+X  X X^2+X X^2  0 X^2+X X^2 X^2 X^2  0 X^2  0  0 X^2+X X^2  X X^2 X^2+X  X X^2 X^2+X  X X^2 X^2+X  X  X X^2 X^2+X  X X^2+X  0 X^2+X X^2+X X^2 X^2  X  X  0  X
 0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  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 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 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+89x^70+442x^71+871x^72+1082x^73+1485x^74+1680x^75+2178x^76+2078x^77+2591x^78+2330x^79+2907x^80+2614x^81+2827x^82+2224x^83+2219x^84+1486x^85+1274x^86+830x^87+692x^88+366x^89+170x^90+160x^91+79x^92+50x^93+10x^94+14x^95+13x^96+2x^97+2x^98+2x^101

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 56.5 seconds.