The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+20x^84+10x^86+64x^87+10x^88+20x^90+1x^96+1x^110+1x^142

The gray image is a linear code over GF(2) with n=174, k=7 and d=84.
This code was found by Heurico 1.16 in 0.094 seconds.