The generator matrix

 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  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  1  1  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  X  0  X  0  X  0  X  0  X  X  X  0  0  X  0  0  X
 0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  0  0  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  0  0  X  0  X  0  X
 0  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  X  X  0  0  0  X  X  X  X  X  0  X  0  0  0  0  X  X  0
 0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  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  0  0  X  X  0  0  0  0  0  X  0  X  X  X  0  0  X  X  0  X  X  X
 0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  0  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  0  0  X  X  X  0  0  X  X  X  0  0  0  0  0  X  0

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+10x^82+15x^84+32x^85+16x^86+32x^87+11x^88+5x^90+5x^92+1x^170

The gray image is a linear code over GF(2) with n=172, k=7 and d=82.
This code was found by Heurico 1.16 in 0.123 seconds.