The generator matrix

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

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+393x^80+774x^82+810x^84+726x^86+429x^88+378x^90+266x^92+138x^94+88x^96+56x^98+28x^100+8x^102+1x^104

The gray image is a linear code over GF(2) with n=344, k=12 and d=160.
This code was found by Heurico 1.11 in 0.593 seconds.