The generator matrix

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

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+50x^84+64x^86+49x^88+54x^90+18x^92+6x^94+3x^96+2x^98+2x^100+2x^102+1x^104+2x^108+2x^112

The gray image is a linear code over GF(2) with n=176, k=8 and d=84.
This code was found by an older version of Heurico in 0 seconds.