The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+224x^78+136x^80+88x^82+34x^84+24x^86+1x^88+2x^92+1x^96+1x^104

The gray image is a linear code over GF(2) with n=320, k=9 and d=156.
This code was found by Heurico 1.16 in 28.8 seconds.