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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+24x^88+4x^90+2x^92+1x^96

The gray image is a linear code over GF(2) with n=344, k=5 and d=176.
This code was found by Heurico 1.16 in 0.334 seconds.