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 X^2  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1
 0  X  0 X^2+X  0 X^2+X  0  X  0 X^2+X X^2+X  0  X  0  0  X  0 X^2+X  0  X  0 X^2+X  0  X  0 X^2+X X^2  X X^2 X^2+X X^2  X  0 X^2+X X^2+X X^2  0 X^2+X X^2+X X^2  0 X^2+X X^2+X X^2  X  0  X X^2  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2  0 X^2  X  X  0 X^2 X^2+X X^2  X X^2 X^2 X^2+X X^2+X  0 X^2 X^2  X  X  X X^2+X  0 X^2 X^2  0 X^2 X^2 X^2+X  X  X  X X^2+X  X  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0  0 X^2  0
 0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0  0

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+100x^84+82x^86+386x^88+128x^89+58x^90+128x^91+43x^92+22x^94+45x^96+30x^98+1x^172

The gray image is a linear code over GF(2) with n=356, k=10 and d=168.
This code was found by Heurico 1.16 in 24.5 seconds.