The generator matrix

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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+43x^78+120x^79+157x^80+162x^81+183x^82+178x^83+142x^84+138x^85+172x^86+154x^87+152x^88+134x^89+88x^90+118x^91+50x^92+14x^93+21x^94+6x^95+8x^96+1x^98+2x^102+1x^110+2x^112+1x^126

The gray image is a linear code over GF(2) with n=340, k=11 and d=156.
This code was found by Heurico 1.16 in 0.629 seconds.