The generator matrix

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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+73x^80+54x^82+245x^84+64x^85+206x^86+128x^87+70x^88+64x^89+18x^90+58x^92+42x^94+1x^164

The gray image is a linear code over GF(2) with n=344, k=10 and d=160.
This code was found by Heurico 1.16 in 0.574 seconds.