The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+245x^76+200x^78+199x^80+176x^82+170x^84+8x^86+5x^88+13x^92+1x^96+1x^104+4x^108+1x^112

The gray image is a linear code over GF(2) with n=320, k=10 and d=152.
This code was found by Heurico 1.16 in 0.328 seconds.