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  1  1  1  1  1  1  X
 0  X  0  0  0  X X^2+X X^2+X  0  0  0  0 X^2+X  X  X X^2+X  0  0  X X^2+X  0  X X^2+X  0 X^2  X X^2+X X^2+X X^2  0 X^2 X^2+X  X  X X^2  0 X^2  X X^2+X X^2 X^2+X  X X^2+X X^2+X  0  0 X^2 X^2 X^2 X^2  X X^2+X X^2+X X^2  X X^2  X X^2  X  0  X  0  X  0 X^2 X^2+X  X  0 X^2+X X^2 X^2  X  0  X X^2  X  0 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X  X  X  X X^2  0  0
 0  0  X  0  X  X  X X^2 X^2 X^2  X  X  X  X  0 X^2  0 X^2  X  X  X  0 X^2  X X^2 X^2+X  0 X^2+X  0 X^2+X  X X^2 X^2 X^2+X X^2  X X^2 X^2 X^2+X X^2+X  0 X^2+X  X  0 X^2+X X^2 X^2+X X^2  X X^2 X^2+X X^2  0  0 X^2+X  X X^2  0 X^2+X X^2  X  X X^2 X^2+X X^2+X X^2+X X^2  0  X  0  0  X  0 X^2+X X^2+X X^2 X^2+X  X X^2  X X^2+X X^2  0 X^2+X  X X^2  X X^2+X X^2
 0  0  0  X  X  0  X  X  X X^2  X X^2 X^2  X  X X^2  0  X  0  X X^2  X X^2 X^2+X  0  0  0 X^2+X  X  X X^2 X^2+X X^2+X  X  X X^2+X X^2  0  0  0 X^2+X  0 X^2+X  0 X^2  0  X X^2+X  X X^2+X X^2 X^2+X X^2  0  X  0 X^2+X X^2+X X^2+X  0 X^2  0 X^2 X^2+X  X X^2  0 X^2+X  0  X X^2+X X^2  X X^2 X^2+X X^2  X X^2+X  0 X^2+X X^2+X  X  X X^2+X X^2+X  X X^2  0  X
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  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+106x^84+96x^86+188x^88+256x^89+160x^90+134x^92+64x^94+18x^96+1x^176

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 0.794 seconds.