The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+46x^69+130x^70+232x^71+314x^72+426x^73+668x^74+764x^75+1081x^76+1196x^77+1279x^78+1418x^79+1341x^80+1534x^81+1308x^82+1198x^83+1024x^84+698x^85+563x^86+384x^87+263x^88+162x^89+128x^90+84x^91+51x^92+28x^93+11x^94+14x^95+16x^96+6x^97+7x^98+2x^99+4x^100+1x^102+1x^104+1x^114

The gray image is a linear code over GF(2) with n=320, k=14 and d=138.
This code was found by Heurico 1.16 in 20.3 seconds.