The generator matrix

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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+92x^82+212x^84+162x^86+157x^88+112x^90+78x^92+50x^94+38x^96+34x^98+37x^100+10x^102+12x^104+14x^106+7x^108+6x^110+2x^116

The gray image is a linear code over GF(2) with n=178, k=10 and d=82.
This code was found by Heurico 1.16 in 0.339 seconds.