The generator matrix

1 0 0 0 0 1 1 1 0 0 X 1 1 X 1 1 1 1 X 1 0 1 X 1 1 0 0 1 1 1 X 1 X 1 1 0 1 0 X X 0 X 1 0 1 X 0 1 0 1 1 0 0 1 X 1 X 1 0 X X 1 1 X X X 1 1 1 1 0 0 1 X 1 0 1 1 0 X 1 1 1 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 X 1 X+1 1 1 1 X+1 1 X+1 1 1 1 1 X X+1 1 X 1 1 X+1 X X 0 X 1 X 1 0 1 X X 1 X 1 X X X 1 X+1 1 0 0 X+1 X 1 1 X+1 1 X 1 X 1 X+1 X 1 1 X X+1 X 0 1 1 1 1 0 0 0 0 X 1
0 0 1 0 0 0 1 1 1 X 1 1 0 1 0 1 1 X X+1 X X+1 0 1 X+1 0 X X+1 X+1 X+1 X+1 X+1 X+1 X 0 X+1 0 X X 1 X 1 0 X X 0 1 1 X 0 1 X 1 0 0 X+1 X 1 X 1 X X X+1 X+1 0 0 1 1 X+1 0 1 X+1 1 0 1 X+1 X X X+1 X 0 X X+1 1 X+1 1
0 0 0 1 0 1 X X+1 1 1 0 0 X X+1 X+1 X+1 1 X X+1 X+1 X 0 1 1 1 1 0 0 1 X X+1 X+1 0 X+1 X+1 1 0 1 X+1 1 X 0 X+1 X+1 X 0 X X 1 0 1 0 0 0 X 0 1 1 X 0 X 0 1 1 X X+1 X X X+1 1 0 X+1 1 1 0 0 X X+1 X 1 1 1 1 X 1
0 0 0 0 1 X 0 X X 1 1 X+1 1 X+1 X+1 X+1 1 X+1 0 X X+1 X X+1 0 X+1 X X X+1 1 X X X 1 X X+1 X X X+1 0 X+1 X+1 X+1 X+1 X X+1 X X X+1 1 X+1 X X X X+1 1 X 1 1 1 X 0 X X 1 1 X X 1 0 X 1 X X 1 1 X+1 0 0 X X 1 0 0 0 X+1

generates a code of length 85 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+98x^78+189x^80+174x^82+159x^84+106x^86+101x^88+44x^90+35x^92+30x^94+23x^96+18x^98+26x^100+6x^102+10x^104+4x^106

The gray image is a linear code over GF(2) with n=170, k=10 and d=78.
This code was found by Heurico 1.10 in 0.078 seconds.