The generator matrix

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

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+124x^69+484x^70+942x^71+1473x^72+2042x^73+2723x^74+3288x^75+3897x^76+4582x^77+4991x^78+5456x^79+5569x^80+5246x^81+5178x^82+4810x^83+4082x^84+3416x^85+2452x^86+1818x^87+1273x^88+714x^89+445x^90+244x^91+139x^92+62x^93+41x^94+16x^95+12x^96+6x^97+6x^98+2x^99+2x^100

The gray image is a linear code over GF(2) with n=320, k=16 and d=138.
This code was found by Heurico 1.13 in 65.8 seconds.